Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation

doi:10.1088/1674-1056/ac1e0b

Abstract Rank-1 attractors play a vital role in biological systems and the circuit systems. In this paper, we consider a periodically kicked Chua model with two delays in a circuit system. We first analyze the local stability of the equilibria of the Chua system and obtain the existence conditions of supercritical Hopf bifurcations. Then, we derive some explicit formulas about Hopf bifurcation, which could help us find the form of Hopf bifurcation and the stability of bifurcating period solutions through the Hassards method. Also, we show that rank-1 chaos occurs when the Chua model with two delays undergoes a supercritical Hopf bifurcation and encounters a periodic kick, which shows the effect of two delays on the circuit system. Finally, we illustrate the theoretical analysis by simulations and try to explain the mechanism of delay in our system.

Keywords: rank one chaos periodically kicked Chua model time delay

Received: 04 April 2021
Revised: 27 July 2021
Accepted manuscript online: 17 August 2021

PACS:	02.30.–f
	02.30.Ks	(Delay and functional equations)
	02.30.Oz	(Bifurcation theory)
	02.30.Sa	(Functional analysis)

Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772291 and 12002297), Youth Talent Support Project of Henan, China (Grant No. 2020HYTP012), Basic Research Project of Universities in Henan Province, China (Grant No. 21zx009), Program for Science& Technology Innovation Talents in Universities of Henan Province, China (Grant No. 22HASTIT018).

Corresponding Authors: Wenjie Yang
E-mail: ywjwm123@foxmail.com

Cite this article:

Wenjie Yang(杨文杰) Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation 2022 Chin. Phys. B 31 020201

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Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation

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