Dynamics analysis and numerical simulations of a new 5D Lorenz-type chaos dynamical system

Volume 10, Issue 11, pp 5976--5984 http://dx.doi.org/10.22436/jnsa.010.11.34

Publication Date: November 24, 2017 Submission Date: August 28, 2017

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Authors

Fuchen Zhang - College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, People's Republic of China. - Mathematical Postdoctoral station, College of Mathematics and Statistics, Southwest University, Chongqing 400716, People’s Republic of China. Xiaofeng Liao - College of Electronic and Information Engineering, Southwest University, Chongqing 400715, People's Republic of China. Chunlai Mu - College of Mathematics and Statistics, Chongqing University, Chongqing 401331, People's Republic of China. Guangyun Zhang - College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, People's Republic of China. Xiaomin Li - College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, People's Republic of China.

Abstract

Ultimate bound sets of chaotic systems have important applications in chaos control and chaos synchronization. Ultimate bound sets can also be applied in estimating the dimensions of chaotic attractors. However, it is often a difficult work to obtain the bounds of high-order chaotic systems due to complex algebraic structure of high-order chaotic systems. In this paper, a new 5D autonomous quadratic chaotic system which is different from the Lorenz chaotic system is proposed and analyzed. Ultimate bound sets and globally exponential attractive sets of this system are studied by introducing the Lyapunov-like functions. To validate the ultimate bound estimation, numerical simulations are also investigated.

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Keywords

• Lorenz-type system
• Lyapunov exponents
• Lyapunov stability
• chaotic attractor
• ultimate bound estimation

MSC

•  65P20
•  65P30
•  65P40
•  34D40

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