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

doi:10.1088/1674-1056/ac1e0b

中国物理B ›› 2022, Vol. 31 ›› Issue (2): 20201-020201.doi: 10.1088/1674-1056/ac1e0b

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

Wenjie Yang(杨文杰)^†

School of Science, Xuchang University, Xuchang 461000, China

收稿日期:2021-04-04 修回日期:2021-07-27 接受日期:2021-08-17 出版日期:2022-01-13 发布日期:2022-01-13
通讯作者: Wenjie Yang E-mail:ywjwm123@foxmail.com
基金资助:
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).

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

Wenjie Yang(杨文杰)^†

School of Science, Xuchang University, Xuchang 461000, China

Received:2021-04-04 Revised:2021-07-27 Accepted:2021-08-17 Online:2022-01-13 Published:2022-01-13
Contact: Wenjie Yang E-mail:ywjwm123@foxmail.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: rank one chaos, periodically kicked Chua model, time delay

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.

Key words: rank one chaos, periodically kicked Chua model, time delay

中图分类号:

02.30.–f

02.30.Ks (Delay and functional equations) 02.30.Oz (Bifurcation theory) 02.30.Sa (Functional analysis)

Wenjie Yang(杨文杰). Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation[J]. 中国物理B, 2022, 31(2): 20201-020201.

Wenjie Yang(杨文杰). Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation[J]. Chin. Phys. B, 2022, 31(2): 20201-020201.

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

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

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