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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 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 |
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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.
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Received: 07 April 2018
Revised: 20 July 2018
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Gg
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(Control of chaos, applications of chaos)
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05.45.Jn
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(High-dimensional chaos)
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Corresponding Authors:
J P Singh
E-mail: jayprakash1261@gmail.com
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Cite this article:
J P Singh, V T Pham, T Hayat, S Jafari, F E Alsaadi, B K Roy A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control 2018 Chin. Phys. B 27 100501
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