中国物理B ›› 2018, Vol. 27 ›› Issue (10): 100501-100501.doi: 10.1088/1674-1056/27/10/100501

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇    下一篇

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

J P Singh, V T Pham, T Hayat, S Jafari, F E Alsaadi, B K Roy   

  1. 1 Department of Electrical Engineering, National Institute of Technology Silchar, 788010, India;
    2 School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;
    3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
    4 Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;
    5 Ambikar University of Technology, Tehran, 15875-4413, Iran;
    6 Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia
  • 收稿日期:2018-04-07 修回日期:2018-07-20 出版日期:2018-10-05 发布日期:2018-10-05
  • 通讯作者: J P Singh E-mail:jayprakash1261@gmail.com

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

J P Singh1, V T Pham2, T Hayat3,4, S Jafari5, F E Alsaadi6, B K Roy1   

  1. 1 Department of Electrical Engineering, National Institute of Technology Silchar, 788010, India;
    2 School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;
    3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
    4 Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;
    5 Ambikar University of Technology, Tehran, 15875-4413, Iran;
    6 Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia
  • Received:2018-04-07 Revised:2018-07-20 Online:2018-10-05 Published:2018-10-05
  • Contact: J P Singh E-mail:jayprakash1261@gmail.com

摘要:

This paper reports a new simple four-dimensional (4D) hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.

关键词: new hyperjerk chaotic system, stable equilibrium, hidden attractors, adaptive backstepping control, synchronization

Abstract:

This paper reports a new simple four-dimensional (4D) hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.

Key words: new hyperjerk chaotic system, stable equilibrium, hidden attractors, adaptive backstepping control, synchronization

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Gg (Control of chaos, applications of chaos) 05.45.Jn (High-dimensional chaos)