Influence of synaptic plasticity on dynamics of neural mass model：a bifurcation study

Abstract

Neural mass model is a typical nonlinear system with rich and complex dynamics. Up to now, most bifurcation researches of neural mass model (NMM) have focused on the influence of input or connection parameters between subpopulations on the dynamics of NMM. Actually, the synaptic strength is varied temporally, owing to synaptic plasticity, and plays a crucial role in regulating the dynamics of NMM. However, there are no researches on synaptic strength bifurcation analysis of NMM, and how excitatory and inhibitory synaptic plasticity exerts an influence on the dynamics of NMM is still little known. Motivated by this idea, the bifurcation analysis of excitatory and inhibitory synaptic strength of NMM is conducted in this study. Firstly, codimension-one bifurcation analyses of excitatory and inhibitory synaptic strengths are performed, respectively, through which the parameters regions of stability, bistablility, normal and abnormal oscillation are determined. Secondly, codimension-two bifurcation analysis is conducted, through which we can further gain an insight into the influence of the interaction between excitatory and inhibitory synaptic strengths on the dynamics of NMM. Finally, the bifurcation analysis results is verified by the simulation results. This study of bifurcation reveals two kinds of oscillation mechanisms: limit cycle oscillation mechanism and input-induced transition between two states of the bistability.