Sundarapandian Vaidyanathan

180 papers Journal 88Unranked 9

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	Dynamics and Machine Learning Prediction in the Novel Chaotic Financial Firm Model. Int. J. Comput. Intell. Syst. Muhamad Deni Johansyah, Sundarapandian Vaidyanathan, Talal Bonny, Wafaa Al Nassan, Aceng Sambas, Khaled Benkouider, Bob Foster
2026	J	`jnl`	Event-Triggered Control for Achievements of Switched Delay Model by Sampling Input. IEEE Access Chang-Hua Lien, Cheng-Ruei Yu, Hao-Chin Chang, Hoang-Giang Nguyen, Sundarapandian Vaidyanathan
2025	J	`jnl`	A New 5-D Hyperchaotic System With a Line Equilibrium, Its Bifurcation Analysis, Circuit Simulation, FPGA Implementation, and Data Prediction Using Long-Term-Short Memory. IEEE Access Talal Bonny, Sundarapandian Vaidyanathan, Wafaa Al Nassan, Aceng Sambas, Fareh Hannachi, Maher Alrahhal, Chittineni Aruna
2025	J	`jnl`	Analysis and Numerical Simulations of Thermofluid Dynamic Characteristics in Duct Systems Under Radiation-Convection Coupling Effects. IEEE Access Hao-Chin Chang, Hung-Chih Li, Chang-Hua Lien, Cheng-Ruei Yu, Chih-Yung Hsu, Sundarapandian Vaidyanathan
2025	J	`jnl`	Event-Triggered Parallel Distributed Compensator Design for Nonlinear System With Mixed Delays and Sampling Input by T-S Fuzzy Approach. IEEE Access Chang-Hua Lien, Hao-Chin Chang, Ker-Wei Yu, Hung-Chih Li, Cheng-Ruei Yu, Sundarapandian Vaidyanathan
2024	J	`jnl`	A New Chaotic System With Two Stable Node-Foci Equilibria and an Unstable Saddle-Focus Equilibrium: Bifurcation and Multistability Analysis, Circuit Design, Voice Cryptosystem Application, and FPGA Implementation. IEEE Access Talal Bonny, Sundarapandian Vaidyanathan, Wafaa Al Nassan, Fareh Hannachi, Aceng Sambas
2024	J	`jnl`	A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption. IEEE Access Aceng Sambas, Miroslav Mahdal, Sundarapandian Vaidyanathan, Brisbane Ovilla-Martínez, Esteban Tlelo-Cuautle, Ahmed A. Abd El-Latif, Bassem Abd-El-Atty, Khaled Benkouider, Talal Bonny
2024	J	`jnl`	Application of Chaotic Signals for Improving the Performance of New Generation Ball Mills. IEEE Access Mükremin Ay, Onur Kalayci, Miroslav Mahdal, Mücahit Turhan, Selçuk Coskun, Fatih Caliskan, Ihsan Pehlivan, Sundarapandian Vaidyanathan
2024	J	`jnl`	Dynamic Analysis and Circuit Design of a New 3D Highly Chaotic System and its Application to Pseudo Random Number Generator (PRNG) and Image Encryption. SN Comput. Sci. Aceng Sambas, Khaled Benkouider, Sezgin Kaçar, Nurdogan Ceylan, Sundarapandian Vaidyanathan, Ibrahim Mohammed Sulaiman, Mohamad Afendee Mohamed, Ahmad Faisal Mohamad Ayob, Sishu Shankar Muni
2024	J	`jnl`	Guest Editorial Machine Learning Technology for Biomedical Signal Processing. IEEE J. Biomed. Health Informatics Aceng Sambas, Sundarapandian Vaidyanathan, Azwa Abdul Aziz
2024	J	`jnl`	Hardware Implementation of a Solar-Powered Buck-Boost Converter for Enhanced Cathodic Protection Using Texas Instruments C2000 Board. IEEE Access Arezki Fekik, Miroslav Mahdal, Mohamed Lamine Hamida, Malek Ghanes, Sundarapandian Vaidyanathan, Amar Bousbaine, Hakim Denoun
2024	J	`jnl`	Modelling, bifurcation analysis, circuit design and FPGA-based implementation of a new chaotic jerk system exhibiting Hopf bifurcations. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Irene M. Moroz, Aceng Sambas, Daniel Clemente-López, Jesús Manuel Muñoz-Pacheco, Jose de Jesus Rangel-Magdaleno
2023	J	`jnl`	A new 4-D hyperchaotic two-scroll system with hidden attractor and its field-programmable gate array implementation. Int. J. Circuit Theory Appl. Sundarapandian Vaidyanathan, Khaled Benkouider, Brisbane Ovilla-Martinez, Esteban Tlelo-Cuautle, Aceng Sambas, P. Darwin
2023	J	`jnl`	Cryptographic applications of a new hyperchaotic system with a hidden attractor. Int. J. Comput. Appl. Technol. Sundarapandian Vaidyanathan, Irene M. Moroz, Aceng Sambas, Bassem Abd-El-Atty, Ahmed A. Abd El-Latif
2023	J	`jnl`	Electronic circuit design and FPGA-based hardware implementation of a new multistable 4-D hyperchaotic four-leaf system. Int. J. Comput. Appl. Technol. Sundarapandian Vaidyanathan, Aceng Sambas, Daniel Clemente-López, Jesús M. Muñoz-Pacheco, Alain Soup Tewa Kammogne, Vannick Fopa Mawamba, Martin Siewe Siewe, Samy Abdelwahab Safaan
2023	J	`jnl`	Highly-secured chaos-based communication system using cascaded masking technique and adaptive synchronization. Multim. Tools Appl. Talal Bonny, Wafaa Al Nassan, Sundarapandian Vaidyanathan, Aceng Sambas
2023	J	`jnl`	Improving Power Quality in Grid-Connected Photovoltaic Systems: A Comparative Analysis of Model Predictive Control in Three-Level and Two-Level Inverters. Sensors Saliha Gada, Arezki Fekik, Miroslav Mahdal, Sundarapandian Vaidyanathan, Ahmed Maidi, Ali Bouhedda
2023	J	`jnl`	Mathematical modelling, bifurcation analysis, circuit design and FPGA implementation of a 5D hyperchaotic weather fluctuation model with a line of equilibrium points. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Irene M. Moroz, Esteban Tlelo-Cuautle, Aceng Sambas, Ciro Fabian Bermudez-Marquez, Samy Abdelwahab Safaan
2023	J	`jnl`	Multistability and Bifurcation Analysis of a Novel 3D Jerk System: Electronic Circuit Design, FPGA Implementation, and Image Cryptography Scheme. IEEE Access Talal Bonny, Sundarapandian Vaidyanathan, Aceng Sambas, Khaled Benkouider, Wafaa Al Nassan, Omar Naqaweh
2022	J	`jnl`	A New 5-D Multistable Hyperchaotic System With Three Positive Lyapunov Exponents: Bifurcation Analysis, Circuit Design, FPGA Realization and Image Encryption. IEEE Access Khaled Benkouider, Sundarapandian Vaidyanathan, Aceng Sambas, Esteban Tlelo-Cuautle, Ahmed A. Abd El-Latif, Bassem Abd-El-Atty, Ciro Fabian Bermudez-Marquez, Ibrahim Mohammed Sulaiman, Aliyu Muhammed Awwal, Poom Kumam
2022	J	`jnl`	A Novel 3D Chaotic System With Line Equilibrium: Multistability, Integral Sliding Mode Control, Electronic Circuit, FPGA Implementation and Its Image Encryption. IEEE Access Aceng Sambas, Sundarapandian Vaidyanathan, Xuncai Zhang, Ismail Koyuncu, Talal Bonny, Murat Tuna, Murat Alçin, Sen Zhang, Ibrahim Mohammed Sulaiman, Aliyu Muhammed Awwal, Poom Kumam
2022	J	`jnl`	Adaptive PID computed-torque control of robot manipulators based on DDPG reinforcement learning. Int. J. Model. Identif. Control. Akram Ghediri, Kheireddine Lamamra, Abdelaziz Ait Kaki, Sundarapandian Vaidyanathan
2022	J	`jnl`	Global stabilisation of control systems using a new sliding mode control method and its application to a general type of synchronisation for chaotic systems. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan
2022	J	`jnl`	Modelling, bifurcation analysis and multistability of a new 4D hyperchaotic system with no balance point, its master-slave synchronisation and MultiSim circuit simulation. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Khaled Benkouider, Aceng Sambas
2021	J	`jnl`	A 5-D Multi-Stable Hyperchaotic Two-Disk Dynamo System With No Equilibrium Point: Circuit Design, FPGA Realization and Applications to TRNGs and Image Encryption. IEEE Access Sundarapandian Vaidyanathan, Aceng Sambas, Bassem Abd-El-Atty, Ahmed A. Abd El-Latif, Esteban Tlelo-Cuautle, Omar Guillén-Fernández, Mustafa Mamat, Mohamad Afendee Mohamed, Murat Alçin, Murat Tuna, Ihsan Pehlivan, Ismail Koyuncu, Mohd Asrul Hery Ibrahim
2021	J	`jnl`	A New 4-D Multi-Stable Hyperchaotic System With No Balance Point: Bifurcation Analysis, Circuit Simulation, FPGA Realization and Image Cryptosystem. IEEE Access Sundarapandian Vaidyanathan, Aceng Sambas, Esteban Tlelo-Cuautle, Ahmed A. Abd El-Latif, Bassem Abd-El-Atty, Omar Guillén-Fernández, Khaled Benkouider, Mohamad Afendee Mohamed, Mustafa Mamat, Mohd Asrul Hery Ibrahim
2021	J	`jnl`	A new conservative chaotic dynamical system with lemniscate equilibrium, its circuit model and FPGA implementation. Int. J. Autom. Control. Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, P. S. Godwin Anand, Aceng Sambas, Omar Guillén-Fernández, Sen Zhang
2021	J	`jnl`	A new multistable jerk system with Hopf bifurcations, its electronic circuit simulation and an application to image encryption. Int. J. Comput. Appl. Technol. Sundarapandian Vaidyanathan, Irene M. Moroz, Ahmed A. Abd El-Latif, Bassem Abd-El-Atty, Aceng Sambas
2021	J	`jnl`	A new super-twisting sliding mode control based direct instantaneous power control of PWM-rectifier connected to grid. Int. J. Model. Identif. Control. Arezki Fekik, Hakim Denoun, Mohamed Lamine Hamida, Sundarapandian Vaidyanathan, Nacera Yassa
2021	J	`jnl`	Chameleon Chaotic Systems With Quadratic Nonlinearities: An Adaptive Finite-Time Sliding Mode Control Approach and Circuit Simulation. IEEE Access Saleh Mobayen, Afef Fekih, Sundarapandian Vaidyanathan, Aceng Sambas
2020	J	`jnl`	A 3-D Multi-Stable System With a Peanut-Shaped Equilibrium Curve: Circuit Design, FPGA Realization, and an Application to Image Encryption. IEEE Access Aceng Sambas, Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, Bassem Abd-El-Atty, Ahmed A. Abd El-Latif, Omar Guillén-Fernández, Sukono, Yuyun Hidayat, Gugun Gundara
2020	J	`jnl`	A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design. Int. J. Model. Identif. Control. Khaled Benkouider, Toufik Bouden, Müstak E. Yalçin, Sundarapandian Vaidyanathan
2020	J	`jnl`	A new family of 9D and 10D hyperchaotic systems from the 8D hyperchaotic Benkouider system, the bifurcation analysis of the 10D hyperchaotic system, circuit design and an application to secure voice communication. Int. J. Model. Identif. Control. Khaled Benkouider, Toufik Bouden, Sundarapandian Vaidyanathan, Müstak E. Yalçin
2020	J	`jnl`	A new four-dimensional two-scroll hyperchaos dynamical system with no rest point, bifurcation analysis, multi-stability, circuit simulation and FPGA design. Int. J. Comput. Appl. Technol. Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, Aceng Sambas, Gervais Dolvis Leutcho, Omar Guillén-Fernández
2020	J	`jnl`	A new multistable hyperjerk dynamical system with self-excited chaotic attractor, its complete synchronisation via backstepping control, circuit simulation and FPGA implementation. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, Aceng Sambas, Gervais Dolvis Leutcho, Omar Guillén-Fernández, Babatunde A. Idowu
2020	J	`jnl`	A novel ANN-based four-dimensional two-disk hyperchaotic dynamical system, bifurcation analysis, circuit realisation and FPGA-based TRNG implementation. Int. J. Comput. Appl. Technol. Sundarapandian Vaidyanathan, Ihsan Pehlivan, Gervais Dolvis Leutcho, Jacques Kengne, Murat Alcin, Murat Tuna, Ismail Koyuncu
2020	J	`jnl`	Adaptive neural-fuzzy and backstepping controller for port-Hamiltonian systems. Int. J. Comput. Appl. Technol. Ahmad Taher Azar, Fernando E. Serrano, Marco A. Flores, Sundarapandian Vaidyanathan, Quanmin Zhu
2020	J	`jnl`	Adaptive self-recurrent wavelet neural network and sliding mode controller/observer for a slider crank mechanism. Int. J. Comput. Appl. Technol. Ahmad Taher Azar, Fernando E. Serrano, Josep M. Rossell, Sundarapandian Vaidyanathan, Quanmin Zhu
2020	J	`jnl`	Complexity, Dynamics, Control, and Applications of Nonlinear Systems with Multistability. Complex. Viet-Thanh Pham, Sundarapandian Vaidyanathan, Tomasz Kapitaniak
2020	J	`jnl`	FPGA design and circuit implementation of a new four-dimensional multistable hyperchaotic system with coexisting attractors. Int. J. Comput. Appl. Technol. Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, Aceng Sambas, Gervais Dolvis Leutcho, Omar Guillén-Fernández
2019	J	`jnl`	A New Double-Wing Chaotic System With Coexisting Attractors and Line Equilibrium: Bifurcation Analysis and Electronic Circuit Simulation. IEEE Access Aceng Sambas, Sundarapandian Vaidyanathan, Sen Zhang, Yicheng Zeng, Mohamad Afendee Mohamed, Mustafa Mamat
2019	—	`conf`	A New Nonlinear Dynamical Model with Three Quadratic Nonlinear Terms and Hidden Chaos. MIPRO Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, Aceng Sambas, Francesco Grasso
2019	J	`jnl`	A memristor-based system with hidden hyperchaotic attractors, its circuit design, synchronisation via integral sliding mode control and an application to voice encryption. Int. J. Autom. Control. Sundarapandian Vaidyanathan, Ahmad Taher Azar, Akif Akgul, Chang-Hua Lien, Sezgin Kaçar, Ünal Çavusoglu
2019	J	`jnl`	A new chaotic dynamical system with a hyperbolic curve of rest points, its complete synchronisation via integral sliding mode control and circuit design. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Aceng Sambas, Chang-Hua Lien, Babatunde A. Idowu
2019	J	`jnl`	A new five-dimensional four-wing hyperchaotic system with hidden attractor, its electronic circuit realisation and synchronisation via integral sliding mode control. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Gervais Dolvis Leutcho, Jacques Kengne, Chang-Hua Lien, Aceng Sambas
2019	J	`jnl`	A new hyperjerk dynamical system with hyperchaotic attractor and two saddle-focus rest points exhibiting Hopf bifurcations, its hyperchaos synchronisation and circuit implementation. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Irene M. Moroz, Aceng Sambas
2019	J	`jnl`	A new robust adaptive fuzzy synergetic control for nonlinear systems with an application to an inverted pendulum. Int. J. Model. Identif. Control. Abderazak Saidi, Farid Naceri, Sundarapandian Vaidyanathan
2019	J	`jnl`	A new switching table based neural network for direct power control of three-phase PWM-rectifier. Int. J. Model. Identif. Control. Arezki Fekik, Hakim Denoun, Mustapha Zaouia, Mohamed Lamine Hamida, Sundarapandian Vaidyanathan
2019	J	`jnl`	A new three-dimensional chaotic system: its adaptive control and circuit design. Int. J. Autom. Control. Sundarapandian Vaidyanathan, Oumate Alhadji Abba, Betchewe Gambo, Alidou Mohamadou
2019	—	`conf`	Adaptive Higher Order Sliding Mode Control for Robotic Manipulators with Matched and Mismatched Uncertainties. AMLTA Ahmad Taher Azar, Fernando E. Serrano, Sundarapandian Vaidyanathan, Hani A. Albalawi
2019	—	`conf`	Adaptive Terminal-Integral Sliding Mode Force Control of Elastic Joint Robot Manipulators in the Presence of Hysteresis. AISI Ahmad Taher Azar, Fernando E. Serrano, Anis Koubaa, Nashwa Ahmad Kamal, Sundarapandian Vaidyanathan, Arezki Fekik
2019	J	`jnl`	Design and implementation of a new cooperative approach to brain tumour identification from MRI images. Int. J. Comput. Appl. Technol. Boucif Beddad, Kaddour Hachemi, Sundarapandian Vaidyanathan
2019	J	`jnl`	Memory Circuit Elements: Complexity, Complex Systems, and Applications. Complex. Viet-Thanh Pham, Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, Tomasz Kapitaniak
2019	J	`jnl`	Real-time high-speed 5-D hyperchaotic Lorenz system on FPGA. Int. J. Comput. Appl. Technol. Ismail Koyuncu, Murat Alçin, Murat Tuna, Ihsan Pehlivan, Metin Varan, Sundarapandian Vaidyanathan
2019	—	`conf`	Robust H-Infinity Decentralized Control for Industrial Cooperative Robots. AISI Ahmad Taher Azar, Fernando E. Serrano, Ibrahim A. Hameed, Nashwa Ahmad Kamal, Sundarapandian Vaidyanathan
2019	J	`jnl`	Robust mixed performance for uncertain Takagi-Sugeno fuzzy time-delay systems with linear fractional perturbations. Int. J. Model. Identif. Control. Chang-Hua Lien, Sundarapandian Vaidyanathan, Ker-Wei Yu, Hao-Chin Chang
2018	J	`jnl`	A new biological snap oscillator: its modelling, analysis, simulations and circuit design. Int. J. Simul. Process. Model. Sundarapandian Vaidyanathan, Moez Feki, Aceng Sambas, Chang-Hua Lien
2018	J	`jnl`	A new chaotic jerk system with two quadratic nonlinearities and its applications to electronic circuit implementation and image encryption. Int. J. Comput. Appl. Technol. Sundarapandian Vaidyanathan, Akif Akgul, Sezgin Kaçar
2018	—	`conf`	A new four-dimensional chaotic system with hidden attractor and its circuit design. LASCAS Sundarapandian Vaidyanathan, Esteban Tlelo-Cuautle, Jesús Manuel Muñoz-Pacheco, Aceng Sambas
2018	J	`jnl`	A new hyperchaotic temperature fluctuations model, its circuit simulation, FPGA implementation and an application to image encryption. Int. J. Simul. Process. Model. Sundarapandian Vaidyanathan, Ahmad Taher Azar, Karthikeyan Rajagopal, Aceng Sambas, Sezgin Kaçar, Ünal Çavusoglu
2018	J	`jnl`	A new three-dimensional chaotic system with a cloud-shaped curve of equilibrium points, its circuit implementation and sound encryption. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Aceng Sambas, Sezgin Kaçar, Ünal Çavusoglu
2018	J	`jnl`	A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation. Int. J. Autom. Control. Sundarapandian Vaidyanathan, Ahmad Taher Azar, Abdesselem Boulkroune
2018	J	`jnl`	A novel four-dimensional conservative chaotic system without linear term, its analysis and adaptive control via integral sliding mode control. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan
2018	J	`jnl`	Development and optimisation of image segmentation algorithm on an embedded DSP-platform. Int. J. Comput. Appl. Technol. Boucif Beddad, Kaddour Hachemi, Sundarapandian Vaidyanathan
2018	J	`jnl`	Discrete Time Sliding Mode Control Scheme for Nonlinear Systems With Bounded Uncertainties. Int. J. Syst. Dyn. Appl. Jalel Ghabi, Ahmed Rhif, Sundarapandian Vaidyanathan
2018	J	`jnl`	Hyperchaotic Attractor in a Novel Hyperjerk System with Two Nonlinearities. Circuits Syst. Signal Process. Peter Daltzis, Sundarapandian Vaidyanathan, Viet-Thanh Pham, Christos K. Volos, Hector E. Nistazakis, George S. Tombras
2018	J	`jnl`	Modelling and simulation of an analytical approach to handle real-time traffic in VoIP network. Int. J. Simul. Process. Model. Sakshi Kaushal, Harish Kumar, Sarbjeet Singh, Shubhani Aggarwal, Jasleen Kaur, Sundarapandian Vaidyanathan
2017	J	`jnl`	A Chaotic Time-Delay System with Saturation Nonlinearity. Int. J. Syst. Dyn. Appl. Viet-Thanh Pham, Christos K. Volos, Sundarapandian Vaidyanathan
2017	—	`ch.`	A Memristor-Based Hyperchaotic System with Hidden Attractor and Its Sliding Mode Control. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	A New Method to Synchronize Fractional Chaotic Systems with Different Dimensions. Fractional Order Control and Synchronization of Chaotic Systems Adel Ouannas, Toufik Ziar, Ahmad Taher Azar, Sundarapandian Vaidyanathan
2017	J	`jnl`	A Novel Chaotic System without Equilibrium: Dynamics, Synchronization, and Circuit Realization. Complex. Ahmad Taher Azar, Christos K. Volos, Nikolaos A. Gerodimos, George S. Tombras, Viet-Thanh Pham, Ahmed G. Radwan, Sundarapandian Vaidyanathan, Adel Ouannas, Jesús M. Muñoz-Pacheco
2017	J	`jnl`	A Novel Four-Dimensional Hyperchaotic Four-Wing System With a Saddle-Focus Equilibrium. IEEE Trans. Circuits Syst. II Express Briefs Christos K. Volos, Jamal-Odysseas Maaita, Sundarapandian Vaidyanathan, Viet-Thanh Pham, Ioannis N. Stouboulos, Ioannis M. Kyprianidis
2017	—	`ch.`	A Three-Dimensional Chaotic System with Square Equilibrium and No-Equilibrium. Fractional Order Control and Synchronization of Chaotic Systems Viet-Thanh Pham, Sundarapandian Vaidyanathan, Christos K. Volos, Sajad Jafari, Tomás Gotthans
2017	—	`ch.`	A Three-Dimensional No-Equilibrium Chaotic System: Analysis, Synchronization and Its Fractional Order Form. Fractional Order Control and Synchronization of Chaotic Systems Viet-Thanh Pham, Sundarapandian Vaidyanathan, Christos K. Volos, Ahmad Taher Azar, Thang Manh Hoang, Vu Van Yem
2017	J	`jnl`	A new fractional hybrid chaos synchronisation. Int. J. Model. Identif. Control. Adel Ouannas, Ahmad Taher Azar, Sundarapandian Vaidyanathan
2017	J	`jnl`	A novel four-leaf chaotic system, its control and synchronisation via integral sliding mode control. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Ahmed Rhif
2017	—	`ch.`	Adaptive Control of a Novel Nonlinear Double Convection Chaotic System. Fractional Order Control and Synchronization of Chaotic Systems Sundarapandian Vaidyanathan, Quanmin Zhu, Ahmad Taher Azar
2017	—	`ch.`	Adaptive Integral Sliding Mode Control of a Chemical Chaotic Reactor System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Adaptive Integral Sliding Mode Controller Design for the Control and Synchronization of a Novel Jerk Chaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Adaptive Integral Sliding Mode Controller Design for the Control and Synchronization of a Rod-Type Plasma Torch Chaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Adaptive Integral Sliding Mode Controller Design for the Control of a Novel 6-D Coupled Double Convection Hyperchaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Adaptive Integral Sliding Mode Controller Design for the Regulation and Synchronization of a Novel Hyperchaotic Finance System with a Stable Equilibrium. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities, Its Adaptive Feedback Control and Synchronization. Fractional Order Control and Synchronization of Chaotic Systems Sundarapandian Vaidyanathan, Ahmad Taher Azar, Adel Ouannas
2017	J	`jnl`	Analysis, synchronisation and circuit implementation of a novel jerk chaotic system and its application for voice encryption. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Aceng Sambas, Mustafa Mamat, W. S. Mada Sanjaya
2017	J	`jnl`	Anti-synchronisation of identical chaotic systems via novel sliding control and its application to a novel chaotic system. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Sivaperumal Sampath
2017	—	`book`	Applications of Sliding Mode Control in Science and Engineering Sundarapandian Vaidyanathan, Chang-Hua Lien
2017	—	`ch.`	Chaotic System Modelling Using a Neural Network with Optimized Structure. Fractional Order Control and Synchronization of Chaotic Systems Kheireddine Lamamra, Sundarapandian Vaidyanathan, Ahmad Taher Azar, Chokri Ben Salah
2017	—	`ch.`	Chattering Free Sliding Mode Controller Design for a Quadrotor Unmanned Aerial Vehicle. Applications of Sliding Mode Control Nour Ben Ammar, Soufiene Bouallègue, Joseph Haggège, Sundarapandian Vaidyanathan
2017	—	`ch.`	Complete Synchronization of Chaotic Systems via Novel Second Order Sliding Mode Control with an Application to a Novel Three-Scroll Chaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Control and Synchronization of a Novel Hyperchaotic Two-Disk Dynamo System via Adaptive Integral Sliding Mode Control. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Fractional Inverse Generalized Chaos Synchronization Between Different Dimensional Systems. Fractional Order Control and Synchronization of Chaotic Systems Adel Ouannas, Ahmad Taher Azar, Toufik Ziar, Sundarapandian Vaidyanathan
2017	—	`book`	Fractional Order Control and Synchronization of Chaotic Systems Ahmad Taher Azar, Sundarapandian Vaidyanathan, Adel Ouannas
2017	J	`jnl`	Fractional-Order and Memristive Nonlinear Systems: Advances and Applications. Complex. Ahmed G. Radwan, Ahmad Taher Azar, Sundarapandian Vaidyanathan, Jesús M. Muñoz-Pacheco, Adel Ouannas
2017	—	`ch.`	Global Stabilization of Nonlinear Systems via Novel Second Order Sliding Mode Control with an Application to a Novel Highly Chaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Hyperchaos and Adaptive Control of a Novel Hyperchaotic System with Two Quadratic Nonlinearities. Fractional Order Control and Synchronization of Chaotic Systems Sundarapandian Vaidyanathan, Ahmad Taher Azar, Adel Ouannas
2017	J	`jnl`	LabVIEW implementation of chaotic masking with adaptively synchronised forced Van der Pol oscillators and its application in real-time image encryption. Int. J. Simul. Process. Model. Sundarapandian Vaidyanathan, Karthikeyan Rajagopal
2017	J	`jnl`	New hybrid synchronisation schemes based on coexistence of various types of synchronisation between master-slave hyperchaotic systems. Int. J. Comput. Appl. Technol. Adel Ouannas, Ahmad Taher Azar, Sundarapandian Vaidyanathan
2017	—	`ch.`	Novel Second Order Sliding Mode Control Design for the Anti-synchronization of Chaotic Systems with an Application to a Novel Four-Wing Chaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	On New Fractional Inverse Matrix Projective Synchronization Schemes. Fractional Order Control and Synchronization of Chaotic Systems Adel Ouannas, Ahmad Taher Azar, Toufik Ziar, Sundarapandian Vaidyanathan
2017	J	`jnl`	On a simple approach for Q-S synchronisation of chaotic dynamical systems in continuous-time. Int. J. Comput. Sci. Math. Adel Ouannas, Ahmad Taher Azar, Sundarapandian Vaidyanathan
2017	—	`ch.`	Particle Swarm Optimization Based Sliding Mode Control Design: Application to a Quadrotor Vehicle. Applications of Sliding Mode Control Alessandro Baldini, Lucio Ciabattoni, Riccardo Felicetti, Francesco Ferracuti, Alessandro Freddi, Andrea Monteriù, Sundarapandian Vaidyanathan
2017	—	`ch.`	Robust Control of a Photovoltaic Battery System via Fuzzy Sliding Mode Approach. Applications of Sliding Mode Control Alessandro Baldini, Lucio Ciabattoni, Riccardo Felicetti, Francesco Ferracuti, Alessandro Freddi, Andrea Monteriù, Sundarapandian Vaidyanathan
2017	—	`ch.`	Sliding Mode Control Design for a Sensorless Sun Tracker. Applications of Sliding Mode Control Ahmed Rhif, Sundarapandian Vaidyanathan
2017	—	`ch.`	Super-Twisting Sliding Mode Control and Synchronization of Moore-Spiegel Thermo-Mechanical Chaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Super-Twisting Sliding Mode Control of the Enzymes-Substrates Biological Chaotic System. Applications of Sliding Mode Control Sundarapandian Vaidyanathan
2017	—	`ch.`	Terminal Sliding Mode Controller Design for a Quadrotor Unmanned Aerial Vehicle. Applications of Sliding Mode Control Rabii Fessi, Soufiene Bouallègue, Joseph Haggège, Sundarapandian Vaidyanathan
2016	—	`ch.`	A 3-D Novel Jerk Chaotic System and Its Application in Secure Communication System and Mobile Robot Navigation. Advances and Applications in Chaotic Systems Aceng Sambas, Sundarapandian Vaidyanathan, Mustafa Mamat, W. S. Mada Sanjaya, Darmawan Setia Rahayu
2016	—	`ch.`	A Chaotic Hyperjerk System Based on Memristive Device. Advances and Applications in Chaotic Systems Viet-Thanh Pham, Sundarapandian Vaidyanathan, Christos K. Volos, Sajad Jafari, Xiong Wang
2016	J	`jnl`	A Chaotic System With Equilibria Located on the Rounded Square Loop and Its Circuit Implementation. IEEE Trans. Circuits Syst. II Express Briefs Viet-Thanh Pham, Sajad Jafari, Christos K. Volos, Aggelos Giakoumis, Sundarapandian Vaidyanathan, Tomasz Kapitaniak
2016	J	`jnl`	A Chaotic System with Different Families of Hidden Attractors. Int. J. Bifurc. Chaos Viet-Thanh Pham, Christos K. Volos, Sajad Jafari, Sundarapandian Vaidyanathan, Tomasz Kapitaniak, Xiong Wang
2016	—	`ch.`	A Novel 2-D Chaotic Enzymes-Substrates Reaction System and Its Adaptive Backstepping Control. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel 3-D Circulant Chaotic System with Labyrinth Chaos and Its Adaptive Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel 3-D Conservative Jerk Chaotic System with Two Quadratic Nonlinearities and Its Adaptive Control. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel 4-D Four-Wing Chaotic System with Four Quadratic Nonlinearities and Its Synchronization via Adaptive Control Method. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Ahmad Taher Azar
2016	—	`ch.`	A Novel 4-D Hyperchaotic Chemical Reactor System and Its Adaptive Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan, Abdesselem Boulkroune
2016	—	`ch.`	A Novel 4-D Hyperchaotic Thermal Convection System and Its Adaptive Control. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel 5-D Hyperchaotic System with a Line of Equilibrium Points and Its Adaptive Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel Conservative Jerk Chaotic System With Two Cubic Nonlinearities and Its Adaptive Backstepping Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan, Christos K. Volos
2016	—	`ch.`	A Novel Design Approach of a Nonlinear Resistor Based on a Memristor Emulator. Advances in Chaos Theory and Intelligent Control Christos K. Volos, Sundarapandian Vaidyanathan, Viet-Thanh Pham, Jamal-Odysseas Maaita, Aggelos Giakoumis, Ioannis M. Kyprianidis, Ioannis N. Stouboulos
2016	—	`ch.`	A Novel Double Convection Chaotic System, Its Analysis, Adaptive Control and Synchronization. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel Highly Hyperchaotic System and Its Adaptive Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	A Novel Hyperjerk System with Two Quadratic Nonlinearities and Its Adaptive Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	A Seven-Term Novel 3-D Jerk Chaotic System with Two Quadratic Nonlinearities and Its Adaptive Backstepping Control. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	A Seven-Term Novel Jerk Chaotic System and Its Adaptive Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	Adaptive Backstepping Control and Synchronization of a Novel 3-D Jerk System with an Exponential Nonlinearity. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Ahmad Taher Azar
2016	—	`ch.`	Adaptive Backstepping Control, Synchronization and Circuit Simulation of a Novel Jerk Chaotic System with a Quartic Nonlinearity. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan, Viet-Thanh Pham, Christos K. Volos
2016	—	`ch.`	Adaptive Control and Circuit Simulation of a Novel 4-D Hyperchaotic System with Two Quadratic Nonlinearities. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan, Christos K. Volos, Viet-Thanh Pham
2016	—	`ch.`	Adaptive Control and Synchronization of Halvorsen Circulant Chaotic Systems. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Ahmad Taher Azar
2016	—	`ch.`	Adaptive Control and Synchronization of a Rod-Type Plasma Torch Chaotic System via Backstepping Control Method. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`book`	Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan, Christos K. Volos
2016	—	`book`	Advances in Chaos Theory and Intelligent Control Advances in Chaos Theory and Intelligent Control Ahmad Taher Azar, Sundarapandian Vaidyanathan
2016	—	`ch.`	Analysis, Adaptive Control and Synchronization of a Novel 3-D Chaotic System with a Quartic Nonlinearity and Two Quadratic Nonlinearities. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	Analysis, Adaptive Control and Synchronization of a Novel 3-D Chaotic System with a Quartic Nonlinearity. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	Analysis, Adaptive Control and Synchronization of a Novel 3-D Highly Chaotic System. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	Analysis, Control and Circuit Simulation of a Novel 3-D Finance Chaotic System. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan, Christos K. Volos, O. I. Tacha, Ioannis M. Kyprianidis, Ioannis N. Stouboulos, Viet-Thanh Pham
2016	—	`ch.`	Analysis, Control and Synchronization of a Novel 4-D Highly Hyperchaotic System with Hidden Attractors. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	J	`jnl`	Analysis, adaptive control and circuit simulation of a novel nonlinear finance system. Appl. Math. Comput. O. I. Tacha, Christos K. Volos, Ioannis M. Kyprianidis, Ioannis N. Stouboulos, Sundarapandian Vaidyanathan, Viet-Thanh Pham
2016	—	`ch.`	Complete Synchronization of Hyperchaotic Systems via Novel Sliding Mode Control. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Sivaperumal Sampath
2016	—	`ch.`	Control of Shimizu-Morioka Chaotic System with Passive Control, Sliding Mode Control and Backstepping Design Methods: A Comparative Analysis. Advances and Applications in Chaotic Systems Ugur Erkin Kocamaz, Yilmaz Uyaroglu, Sundarapandian Vaidyanathan
2016	J	`jnl`	Design of a Chaotic Random Bit Generator Using a Duffing - van der Pol System. Int. J. Syst. Dyn. Appl. Christos K. Volos, Ioannis M. Kyprianidis, Ioannis N. Stouboulos, Sundarapandian Vaidyanathan
2016	—	`ch.`	Dynamic Analysis, Adaptive Control and Synchronization of a Novel Highly Chaotic System with Four Quadratic Nonlinearities. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	Dynamic Analysis, Adaptive Feedback Control and Synchronization of An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Ahmad Taher Azar
2016	—	`ch.`	Dynamics, Synchronization and SPICE Implementation of a Memristive System with Hidden Hyperchaotic Attractor. Advances in Chaos Theory and Intelligent Control Viet-Thanh Pham, Sundarapandian Vaidyanathan, Christos K. Volos, Thang Manh Hoang, Vu Van Yem
2016	—	`ch.`	Fuzzy Adaptive Synchronization of Incommensurate Fractional-Order Chaotic Systems. Advances and Applications in Chaotic Systems Amel Bouzeriba, Abdesselem Boulkroune, Toufik Bouden, Sundarapandian Vaidyanathan
2016	—	`ch.`	Fuzzy Control-Based Function Synchronization of Unknown Chaotic Systems with Dead-Zone Input. Advances in Chaos Theory and Intelligent Control Abdesselem Boulkroune, Sarah Hamel, Ahmad Taher Azar, Sundarapandian Vaidyanathan
2016	—	`ch.`	Generalized Projective Synchronization of a Novel Chaotic System with a Quartic Nonlinearity via Adaptive Control. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan, Sarasu Pakiriswamy
2016	—	`ch.`	Generalized Projective Synchronization of a Novel Hyperchaotic Four-Wing System via Adaptive Control Method. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Ahmad Taher Azar
2016	—	`ch.`	Global Chaos Control and Synchronization of a Novel Two-Scroll Chaotic System with Three Quadratic Nonlinearities. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	Global Chaos Synchronization of a Novel 3-D Chaotic System with Two Quadratic Nonlinearities via Active and Adaptive Control. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	Hyperchaos, Control, Synchronization and Circuit Simulation of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Christos K. Volos, Viet-Thanh Pham
2016	—	`ch.`	Qualitative Analysis and Adaptive Control of a Novel 4-D Hyperchaotic System. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	Qualitative Analysis and Properties of a Novel 4-D Hyperchaotic System with Two Quadratic Nonlinearities and Its Adaptive Control. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan
2016	—	`ch.`	Qualitative Study and Adaptive Control of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities. Advances in Chaos Theory and Intelligent Control Sundarapandian Vaidyanathan, Ahmad Taher Azar
2016	—	`ch.`	Sliding Mode Controller Design for the Global Stabilization of Chaotic Systems and Its Application to Vaidyanathan Jerk System. Advances and Applications in Chaotic Systems Sundarapandian Vaidyanathan
2016	—	`ch.`	Synchronization Phenomena in Coupled Hyperchaotic Oscillators with Hidden Attractors Using a Nonlinear Open Loop Controller. Advances and Applications in Chaotic Systems Christos K. Volos, Viet-Thanh Pham, Sundarapandian Vaidyanathan, Ioannis M. Kyprianidis, Ioannis N. Stouboulos
2016	J	`jnl`	Takagi-Sugeno fuzzy logic controller for Liu-Chen four-scroll chaotic system. Int. J. Intell. Eng. Informatics Sundarapandian Vaidyanathan, Ahmad Taher Azar
2015	—	`ch.`	Analysis and Control of a 4-D Novel Hyperchaotic System. Chaos Modeling and Control Systems Design Sundarapandian Vaidyanathan, Ahmad Taher Azar
2015	—	`ch.`	Analysis, Control and Synchronization of a Nine-Term 3-D Novel Chaotic System. Chaos Modeling and Control Systems Design Sundarapandian Vaidyanathan, Ahmad Taher Azar
2015	J	`jnl`	Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan
2015	—	`ch.`	Anti-synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan-Madhavan Chaotic Systems. Advances and Applications in Sliding Mode Control Systems Sundarapandian Vaidyanathan, Ahmad Taher Azar
2015	—	`ch.`	Backstepping Controller Design for the Global Chaos Synchronization of Sprott's Jerk Systems. Chaos Modeling and Control Systems Design Sundarapandian Vaidyanathan, Babatunde A. Idowu, Ahmad Taher Azar
2015	—	`book`	Chaos Modeling and Control Systems Design Chaos Modeling and Control Systems Design Ahmad Taher Azar, Sundarapandian Vaidyanathan
2015	—	`book`	Computational Intelligence Applications in Modeling and Control Computational Intelligence Applications in Modeling and Control Ahmad Taher Azar, Sundarapandian Vaidyanathan
2015	J	`jnl`	Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Ahmad Taher Azar, Karthikeyan Rajagopal, Prasina Alexander
2015	—	`ch.`	Global Chaos Control of a Novel Nine-Term Chaotic System via Sliding Mode Control. Advances and Applications in Sliding Mode Control Systems Sundarapandian Vaidyanathan, Christos K. Volos, Viet-Thanh Pham
2015	J	`jnl`	Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan, Sivaperumal Sampath, Ahmad Taher Azar
2015	—	`ch.`	Hybrid Synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan Chaotic Systems. Advances and Applications in Sliding Mode Control Systems Sundarapandian Vaidyanathan, Ahmad Taher Azar
2015	J	`jnl`	Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan
2015	—	`ch.`	Multi-scroll Chaotic Oscillator Based on a First-Order Delay Differential Equation. Chaos Modeling and Control Systems Design Viet-Thanh Pham, Christos K. Volos, Sundarapandian Vaidyanathan
2014	J	`jnl`	Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan
2014	J	`jnl`	Generalised projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan
2014	J	`jnl`	Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control. Int. J. Model. Identif. Control. Sundarapandian Vaidyanathan
2012	—	`conf`	Analysis and Synchronization of the Hyperchaotic Yujun Systems via Sliding Mode Control. ACITY (1) Sundarapandian Vaidyanathan
2012	—	`conf`	Analysis, Control and Synchronization of Hyperchaotic Zhou System via Adaptive Control. ACITY (2) Sundarapandian Vaidyanathan
2012	J	`jnl`	Anti-synchronization of four-wing chaotic systems via sliding mode control. Int. J. Autom. Comput. Sundarapandian Vaidyanathan, Sivaperumal Sampath
2012	—	`conf`	Global chaos synchronization of Arneodo chaotic system via backstepping controller design. CCSEIT Sundarapandian Vaidyanathan
2011	—	`conf`	The Design of Active Feedback Controllers for the Generalized Projective Synchronization of Hyperchaotic Qi and Hyperchaotic Lorenz Systems. CISIM Sundarapandian Vaidyanathan, Sarasu Pakiriswamy
2005	J	`jnl`	Distributed control schemes for large-scale interconnected discrete-time linear systems. Math. Comput. Model. Sundarapandian Vaidyanathan
2005	J	`jnl`	Observer design and stabilization of the dominant state of discrete-time linear systems. Math. Comput. Model. Sundarapandian Vaidyanathan