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Controlling Dynamics to Coexisting Periodic Solutions or Equilibrium Points of the $n$ $n$ -Scroll Modified Chua’s Circuit

Shihui Fu

http://orcid.org/0000-0003-0682-4556

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China

E-mail Address: fshtp@163.com

Corresponding author.

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Ying Han

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China

E-mail Address: 2268357744@qq.com

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Huizhen Ma

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China

E-mail Address: 2470362604@qq.com

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, and

Ying Du

School of Science, East China University of Science and Technology, Shanghai 200237, P. R. China

E-mail Address: duying@ecust.edu.cn

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https://doi.org/10.1142/S0218127419501803Cited by:2 (Source: Crossref)

Abstract

The modified Chua’s circuit, which is first order differentiable, has degree-of-discontinuity $3$ $3$ . It has $2 n - 1$ $2 n - 1$ equilibrium points, including two boundary equilibrium points. For them, except boundary equilibrium points, we obtain in theory, conditions under which Hopf bifurcations exist, which implies coexisting periodic solutions. At the same time, we also show that equilibrium points are asymptotically stable when system parameters are within some limits. Furthermore, we theoretically design a linear feedback controller, which will not change the equilibrium points, with appropriate control parameters to control the dynamical behaviors including chaos to these periodic solutions or equilibrium points, and we verify it by numerical simulations.

This paper was supported by National Natural Science Foundation of China (Grant Nos. 11602224, 61873245 and 11672107).

Keywords:

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