QUALITATIVE BEHAVIORS AND CONTROL OF A NEW FOUR-DIMENSIONAL LORENZ SYSTEM

Fuchen Zhang; Song Chen; Xiusu Chen; Fei Xu; Min Xiao

doi:10.11948/20240462

2025 Volume 15 Issue 5

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Fuchen Zhang, Song Chen, Xiusu Chen, Fei Xu, Min Xiao. QUALITATIVE BEHAVIORS AND CONTROL OF A NEW FOUR-DIMENSIONAL LORENZ SYSTEM[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 3025-3044. doi: 10.11948/20240462

Citation:

Fuchen Zhang, Song Chen, Xiusu Chen, Fei Xu, Min Xiao. QUALITATIVE BEHAVIORS AND CONTROL OF A NEW FOUR-DIMENSIONAL LORENZ SYSTEM[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 3025-3044. doi: 10.11948/20240462

QUALITATIVE BEHAVIORS AND CONTROL OF A NEW FOUR-DIMENSIONAL LORENZ SYSTEM

1.
Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2.
School of Economics, Chongqing Finance and Economics College, Longzhouwan, Ba'nan District, Chongqing 401320, China
3.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada
4.
College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Author Bio: Email: chensong19992022@163.com(S. Chen); Email: 1279776835@qq.com(X. Chen); Email: fxu.feixu@gmail.com(F. Xu); Email: candymanxm2003@aliyun.com(M. Xiao)
Corresponding author: Email: zhangfuchen1983@163.com(F. Zhang)

Abstract

Abstract

In this paper, a new nonlinear four-dimensional Lorenz system is proposed. Nonlinear dynamical properties of this system, including the stability of the fixed points, Lyapunov exponents, the bifurcation behaviors and sensitivity to initial conditions, are considered by using chaos theory and numerical simulations. It is very interesting that we find that this system exhibits chaos phenomena for a set of parameters. The globally exponential attractive set of this system has been obtained according to Lyapunov stability theory. Synchronization has been realized between two identical hyperchaotic systems via globally exponential approach and sliding mode control method by using the results of the global exponential attractive set, Vaidyanathan's theorem and Dini derivative. The novelty of the paper lies in that the globally exponential attractive set of the system is obtained firstly, then the result of the globally exponential attractive set is used to study chaos control and chaos synchronization. Furthermore, the precise mathematical expression of the controller is obtained according to the boundedness of this system. Finally, the synchronization process is simulated by MATLAB to illustrate the effectiveness of the theoretical analysis. The results of numerical simulations show that two control methods for chaos synchronization are effective.
- Lorenz system /
- stability theory /
- qualitative theory /
- bifurcation behavior /
- sliding mode control
MSC: 34D06, 34H10, 26A33, 39A13

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References

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