A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control

doi:10.1088/1674-1056/27/4/040503

中国物理B ›› 2018, Vol. 27 ›› Issue (4): 40503-040503.doi: 10.1088/1674-1056/27/4/040503

• TOPIC REVIEW—Thermal and thermoelectric properties of nano materials • 上一篇下一篇

A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control

Jay Prakash Singh, Binoy Krishna Roy, Zhouchao Wei(魏周超)

1. Department of Electrical Engineering, National Institute of Technology Silchar, Silchar 788010, India;
2. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

收稿日期:2017-10-24 修回日期:2017-12-29 出版日期:2018-04-05 发布日期:2018-04-05
通讯作者: Jay Prakash Singh E-mail:jayprakash1261@gmail.com
基金资助:
One of the authors (Dr. Zhouchao Wei) was supported by the National Natural Science Foundation of China (Grant No. 11772306).

A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control

Jay Prakash Singh¹, Binoy Krishna Roy¹, Zhouchao Wei(魏周超)²

1. Department of Electrical Engineering, National Institute of Technology Silchar, Silchar 788010, India;
2. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Received:2017-10-24 Revised:2017-12-29 Online:2018-04-05 Published:2018-04-05
Contact: Jay Prakash Singh E-mail:jayprakash1261@gmail.com
Supported by:
One of the authors (Dr. Zhouchao Wei) was supported by the National Natural Science Foundation of China (Grant No. 11772306).

摘要/Abstract

摘要：

This paper presents a new four-dimensional (4D) autonomous chaotic system which has first Lyapunov exponent of about 22 and is comparatively larger than many existing three-dimensional (3D) and 4D chaotic systems. The proposed system exhibits hyperbolic curve and circular paraboloid types of equilibria. The system has all zero eigenvalues for a particular case of an equilibrium point. The system has various dynamical behaviors like hyperchaotic, chaotic, periodic, and quasi-periodic. The system also exhibits coexistence of attractors. Dynamical behavior of the new system is validated using circuit implementation. Further an interesting switching synchronization phenomenon is proposed for the new chaotic system. An adaptive global integral sliding mode control is designed for the switching synchronization of the proposed system. In the switching synchronization, the synchronization is shown for the switching chaotic, stable, periodic, and hybrid synchronization behaviors. Performance of the controller designed in the paper is compared with an existing controller.

关键词: new hyperchaotic system, maximum chaos, an infinite number of equilibria, hidden attractors, switching synchronization, global sliding mode control

Abstract:

Key words: new hyperchaotic system, maximum chaos, an infinite number of equilibria, hidden attractors, switching synchronization, global sliding mode control

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)

Jay Prakash Singh, Binoy Krishna Roy, 魏周超. A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control[J]. 中国物理B, 2018, 27(4): 40503-040503.

Jay Prakash Singh, Binoy Krishna Roy, Zhouchao Wei(魏周超). A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control[J]. Chin. Phys. B, 2018, 27(4): 40503-040503.

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A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control

A new four-dimensional chaotic system with first Lyapunov exponent of about 22, hyperbolic curve and circular paraboloid types of equilibria and its switching synchronization by an adaptive global integral sliding mode control

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