电场作用下改进HR神经元模型的动力学行为

Dynamical Behavior of an Improved HR Neuron Model Under Electric Field

生物神经细胞内钾、钠和钙离子的跨膜运动将伴随着时变的电磁场,其中激发的电场能够实现对生物神经活动的进一步调制.主要运用非线性理论和数值模拟方案,建立并揭示了一类四维Hindmarsh-Rose(HR)神经元模型的时变稳定性以及全局动力学行为.基于理论分析证实了该非自治的模型存在3种类型的平衡点以及时变稳定性,这也为多吸引子共存提供了理论的依据.此外,得益于双参数分岔图,揭示了该模型的自组织特征,包括“梳”状的混沌结构、倍周期分岔甚至加周期分岔模式.与此同时,神经系统不可避免地受到时变的外界电场扰动,从而导致该模型产生更加复杂的放电活动,并借助于吸引域阐明了丰富的多吸引子共存行为,研究结论可以为进一步探讨外电场效应下神经元复杂的动力学特性提供参考.

The movement of large amounts of ions,sush as potassium,sodium,and calcium ions,in the nervous system triggers time-varying electromagnetic fields that further regulate the firing activity of neurons.'The discharge characteristics of an improved Hindmarsh-Rose(HR)neuron model under electric field are studied by numerical simulation.Based on the theoretical analysis,it is proved that the non-autonomous model has three kinds of equilibrium points and time-varying stability,which also provides a theoretical basis for the coexistence of multiple attractors.In addition,by two-parametric bifurcation analysis,we also find that the model generally has a comb-shaped chaotic structure and a chaotic(or non-chaotic)period-adding bifurcation mode.Considering that the electric field is inevitably disturbed periodically,the discharge mode of this model is more complex and has abundant co-existing oscillation modes.The results will provide a useful reference for further studying on the complex dynamic characteristics of neurons under electric field.