Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2026, Vol. 42 ›› Issue (6): 1063-1072.doi: 10.3969/j.issn.1005-3085.2025.06.006

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Analysis of a Complex Four-dimensional Chaotic System and\\ Its Application

ZHANG Yong1,  ZHANG Fuchen2,  XIAO Min3   

  1. 1. Basic Teaching Department of Henan Polytechnic Institute, Nanyang 473000
    2. School of Mathematics and Statistics, Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring, Chongqing Technology and Business University, Chongqing 400067
    3. College of Artificial Intelligence and College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023
  • Received:2025-03-25 Accepted:2025-07-09 Online:2025-12-15 Published:2026-02-15
  • Contact: F. Zhang. E-mail address: zhangfuchen1983@163.com
  • Supported by:
    The National Natural Science Foundation of China (62073172); the Natural Science Foundation of Jiangsu Province (BK20221329); the Research Project of Henan Province Science and Technology Key Project in 2025 (252102110356); the Sixth Batch of Provincial Science and Technology Research and Development Plan Joint Fund Project (Industry Category) of Henan Provincial Department of Science and Technology in 2024 (245101610063); the Chongqing Education Commission Science and Technology Research Project (KJCX2020037); the Program of Chongqing Technology and Business University (1960288; 2019ZKYYA122); the Teaching Reform Project for Postgraduate Students of Chongqing Technology and Business University (24YJG307); the 2025 Chongqing Higher Education Teaching Reform Research Project (253156).

Abstract:

In this paper, the complex dynamical behaviors of a four-dimensional chaotic system, including boundedness, global attractive domain and Hamiltonian energy function, are studied. We can judge whether the equilibrium point of chaotic system is stable or not according to the result of the globally exponential attractive set. According to the result of the globally exponential attractive set of this system, the equilibrium point of this system is globally exponential stable. As far as the author knows, the study of boundedness and global attraction domain of chaotic systems is mostly limited to low-dimensional chaotic systems, but due to the structural complexity of high-dimensional chaotic systems, there are few studies on the boundedness and the global attraction domain of high-dimensional chaotic systems. The innovation of this paper is that not only the boundedness of a high-dimensional chaotic system is obtained, but also the rate estimation of the attractive domain of the orbit is obtained. The mathematical expression of a cluster of global attractive sets for the chaotic system is obtained. The research results of this paper provide theoretical basis and support for secure communication based on chaos synchronization.

Key words: chaos, stability theory, globally exponential stability, Hamiltonian energy

CLC Number: