Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays

doi:10.1088/1674-1056/aca601

中国物理B ›› 2023, Vol. 32 ›› Issue (3): 38701-038701.doi: 10.1088/1674-1056/aca601

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays

Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军)^†, Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷)

School of Automation and Electronic Information, Xiangtan University, Xiangtan 41110, China

收稿日期:2022-09-02 修回日期:2022-10-24 接受日期:2022-11-25 出版日期:2023-02-14 发布日期:2023-02-21
通讯作者: Zhi-Jun Li E-mail:lizhijun_320@163.com
基金资助:
Project supported by the National Natural Science Foundations of China (Grant Nos. 62171401 and 62071411).

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays

Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军)^†, Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷)

School of Automation and Electronic Information, Xiangtan University, Xiangtan 41110, China

Received:2022-09-02 Revised:2022-10-24 Accepted:2022-11-25 Online:2023-02-14 Published:2023-02-21
Contact: Zhi-Jun Li E-mail:lizhijun_320@163.com
Supported by:
Project supported by the National Natural Science Foundations of China (Grant Nos. 62171401 and 62071411).

摘要/Abstract

摘要： A memristor-coupled heterogenous neural network consisting of two-dimensional (2D) FitzHugh-Nagumo (FHN) and Hindmarsh-Rose (HR) neurons with two time delays is established. Taking the time delays as the control parameters, the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically, and the validity of the Hopf bifurcation condition is verified by numerical analysis. The results show that the two time delays can make the stable equilibrium point unstable, thus leading to periodic oscillations induced by Hopf bifurcation. Furthermore, the time delays in FHN and HR neurons have different effects on the firing activity of neural network. Complex firing patterns, such as quiescent state, chaotic spiking, and periodic spiking can be induced by the time delay in FHN neuron, while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron. Especially, phase synchronization between the heterogeneous neurons is explored, and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron. Finally, the theoretical analysis is verified by circuit simulations.

关键词: memristor, time delay, heterogeneous neurons, hopf bifurcation, phase synchronization

Abstract: A memristor-coupled heterogenous neural network consisting of two-dimensional (2D) FitzHugh-Nagumo (FHN) and Hindmarsh-Rose (HR) neurons with two time delays is established. Taking the time delays as the control parameters, the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically, and the validity of the Hopf bifurcation condition is verified by numerical analysis. The results show that the two time delays can make the stable equilibrium point unstable, thus leading to periodic oscillations induced by Hopf bifurcation. Furthermore, the time delays in FHN and HR neurons have different effects on the firing activity of neural network. Complex firing patterns, such as quiescent state, chaotic spiking, and periodic spiking can be induced by the time delay in FHN neuron, while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron. Especially, phase synchronization between the heterogeneous neurons is explored, and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron. Finally, the theoretical analysis is verified by circuit simulations.

Key words: memristor, time delay, heterogeneous neurons, hopf bifurcation, phase synchronization

中图分类号: (Models of single neurons and networks)

87.19.ll

87.19.lj (Neuronal network dynamics) 05.45.Pq (Numerical simulations of chaotic systems)

Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays[J]. 中国物理B, 2023, 32(3): 38701-038701.

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Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays

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