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Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

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Abstract

This paper studies a four-dimensional (4D) memristive system modified from the 3D chaotic system proposed by Lü and Chen. The new system keeps the symmetry and dissipativity of the original system and has an uncountable infinite number of stable and unstable equilibria. By varying the strength of the memristor, we find rich complex dynamics, such as limit cycles, torus, chaos, and hyperchaos, which can peacefully coexist with the stable equilibria. To explain such coexistence, we compute the unstable manifolds of the equilibria, find that the manifolds create a safe zone for the hyperchaotic attractor, and also find many heteroclinic orbits. To verify the existence of hyperchaos in the 4D memristive circuit, we carry out a computer-assisted proof via a topological horseshoe with two-directional expansions, as well as a circuit experiment on oscilloscope views.

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Acknowledgments

We are very grateful to the reviewers for their valuable comments and suggestions. This work is supported in part by the National Natural Science Foundation of China (61104150), and Science Fund for Distinguished Young Scholars of Chongqing (cstc2013jcyjjq40001), and the Science and Technology Project of Chongqing Education Commission (KJ130517).

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Authors and Affiliations

  1. Key Laboratory of Industrial Internet of Things and Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing,  400065, China

    Qingdu Li

  2. Research Center of Analysis and Control for Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing,  400065, China

    Qingdu Li, Hongzheng Zeng & Jing Li

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  1. Qingdu Li
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  2. Hongzheng Zeng
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Correspondence to Qingdu Li.

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Li, Q., Zeng, H. & Li, J. Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria. Nonlinear Dyn 79, 2295–2308 (2015). https://doi.org/10.1007/s11071-014-1812-4

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