中文摘要：

神经群模型是典型的非线性系统,具有丰富而复杂的动力学行为模式.神经群兴奋性和抑制性突触具有可塑性,并对神经群动力学特性具有重要调控作用,研究突触可塑性对神经群动力学特性的调控规律具有重要意义.本文基于分岔理论,通过神经群模型兴奋性和抑制性突触增益的余维一分岔分析,分别给出了神经群运行于单稳、双稳、正常和异常极限环振荡状态的兴奋性和抑制性突触增益的单参数区间;进而通过兴奋性和抑制性突触增益的余维二分岔分析给出了神经群运行于上述多种状态的双参数区域.上述结果定量剖析了兴奋性与抑制性突触可塑性及二者的相互作用对神经群动力学特性的调控规律,揭示了兴奋性与抑制性的动态平衡在神经电活动调控中所扮演的关键角色,仿真结果验证了分岔分析的正确性.本文的研究对理解突触可塑性在脑功能的维持及各种神经疾病的诱发机制中所扮演的角色具有重要参考价值.

英文摘要：

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.