具有时滞的磁通神经元模型的稳定性及Hopf分岔

doi:10.6040/j.issn.1671-9352.0.2020.586

摘要/Abstract

摘要： 提出一个含磁控忆阻器的时滞磁通神经元模型,研究时滞和外部刺激电流对该模型动力学行为的影响。利用Routh-Hurwitz判据讨论该模型在平衡点处的稳定性,并利用中心流形定理进一步研究该模型在临界点处Hopf分岔的稳定性。通过数值模拟,得到在不同时滞下该模型的时间序列图及单双参分岔图。当改变时滞和外部强迫电流时,发现该模型存在多种放电模式,通过选择合适的时滞或外部强迫电流得到系统的静息态、尖峰放电态和周期簇放电态,这有助于解释电磁辐射所导致的大脑或神经中枢异常放电行为。

关键词: 磁控忆阻器, 时滞, 外部刺激电流, Hopf分岔, 电磁辐射, 双参数分岔

Abstract: A time-delayed flux neuron model with magnetically controlled memristor to study the effects of time delay and external stimulation current on the dynamic behavior of the model is put forward. The stability of the model at the equilibrium point is discussed by using the Routh-Hurwitz criterion and the stability of the Hopf bifurcation at the critical point is further studied by using the central manifold theorem. By numerical stimulation, the time series and single-double bifurcation diagrams of the model with different time delays. When the time lag and external forcing current are changed, it is found that there are many discharge patterns in the model. By selecting appropriate time lag or external forcing current, the resting state, spiking state and periodic bursting state are obtained, which is conducive to explain the abnormal discharge behavior of brain or nerve center caused by electromagnetic radiation.

Key words: magnetically controlled memristors, time delay, external stimulation current, Hopf bifurcation, electromagnetic radiation, two parameter bifurcation

中图分类号:

O441.4

魏立祥,张建刚,南梦冉,张美娇. 具有时滞的磁通神经元模型的稳定性及Hopf分岔[J]. 《山东大学学报(理学版)》, 2021, 56(5): 12-22.

WEI Li-xiang, ZHANG Jian-gang, NAN Meng-ran, ZHANG Mei-jiao. Stability and Hopf bifurcation of a flux neuron model with time delay[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(5): 12-22.

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