双频激励下的两房室神经元模型的动力学分析

Dynamical analysis in a two-compartment model with multiple-periodic excitations

以双频激励下的两房室神经元模型为例,研究了多频激励下的不同激励频率对快慢耦合系统的复杂动力学行为及其产生机制的影响.以一个慢变量表达式建模多个外激励项,将系统转化为耦合的快慢混合系统,从快慢分析的传统观点探索分岔模式及相应分岔行为与慢变参数之间的关系.结果表明当两个激励频率均远小于系统的固有频率时,系统可以产生混合簇振荡行为.本文的结果说明不同的周期激励对系统的分岔结构有着重要影响,快子系统在不同激励频率取值下能够产生多个平衡态和多种分岔共存的现象,从而使得系统存在着混合簇振荡行为.

By taking the controlled two-compartment model with two slow excitation frequencies as an example,the influence of different frequency on the dynamics as well as the generation mechanism of the various complex behaviors is investigated.A slow variable expression is used to model multiple external excitation terms,and the system is transformed into a coupled fast and slow hybrid system.From the traditional point of view of fast and slow analysis,the relationship between bifurcation mode and corresponding bifurcation behavior and slow variable parameters is explored.It is found that the system can generate multi-mode bursting oscillations if there exists an order gap between the exciting frequency and the natural one.Our results show that different frequencies have great influence on the bifurcation structure of the system.It is indicated that both of the multi-equilibria states and various bifurcation behaviors are coexisted in the equilibrium curves,thus further multi-mode bursting oscillations can be observed in the controlled system with different stimulus values.