Constructing hyperchaotic systems at will. (12th February 2015)

• Record Type: Journal Article
• Authors: Shen, Chaowen; Yu, Simin; Lü, Jinhu; Chen, Guanrong
• Is Part Of: International journal of circuit theory and applications. Volume 43:Number 12(2015:Dec.)
• Page Start: 2039
• Page End: 2056
• Publication Date: 2015-02-12
• Subjects: chaotification -- hyperchaotic system -- closed‐loop poles assignment -- DSP realization -- Lyapunov exponents allocation; Electric circuit analysis -- Periodicals; 621.319205
• DOI: 10.1002/cta.2062
• Languages: English
• ISSNs: 0098-9886

Abstract

Summary: Over the last two decades, chaotification has received increasing attention from various communities of science and engineering. This paper aims at developing a unified chaotification framework for generating desired higher‐dimensional dissipative hyperchaotic systems by using a single‐parameter controller. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Specifically, the proposed scheme is to assign desired closed‐loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle‐focus equilibria. For the non‐degenerate case, the number of positive Lyapunov exponents of the controlled system is given by the largest number of positive Lyapunov exponents of the desired hyperchaotic system. Two representative examples are given to illustrate and verify the proposed design method. Finally, the digital signal processor is employed to implement the above 10‐dimensional hyperchaotic systems, and the experimental observation is also given. Copyright © 2015 John Wiley & Sons, Ltd. Abstract : This paper aims at developing a unified chaotification framework for generating desired higher‐dimensional dissipative hyperchaotic systems by using a single‐parameter controller. The scheme is to assign desired closed‐loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle‐focus equilibria. Two representative examples are given and the digital signal processor is employed to implement the two 10‐dimensional hyperchaotic systems, with experimental observation given.