Ge Penghe, Cao Hongjun
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China.
Chaos. 2019 Feb;29(2):023129. doi: 10.1063/1.5053908.
This paper takes into account a neuron network model in which the excitatory and the inhibitory Rulkov neurons interact each other through excitatory and inhibitory chemical coupling, respectively. Firstly, for two or more identical or non-identical Rulkov neurons, the existence conditions of the synchronization manifold of the fixed points are investigated, which have received less attention over the past decades. Secondly, the master stability equation of the arbitrarily connected neuron network under the existence conditions of the synchronization manifold is discussed. Thirdly, taking three identical Rulkov neurons as an example, some new results are presented: (1) topological structures that can make the synchronization manifold exist are given, (2) the stability of synchronization when different parameters change is discussed, and (3) the roles of the control parameters, the ratio, as well as the size of the coupling strength and sigmoid function are analyzed. Finally, for the chemical coupling between two non-identical neurons, the transversal system is given and the effect of two coupling strengths on synchronization is analyzed.
本文考虑了一种神经网络模型，其中兴奋性和抑制性鲁尔科夫神经元分别通过兴奋性和抑制性化学耦合相互作用。首先，对于两个或更多相同或不同的鲁尔科夫神经元，研究了不动点同步流形的存在条件，这在过去几十年中受到的关注较少。其次，讨论了在同步流形存在条件下任意连接神经网络的主稳定性方程。第三，以三个相同的鲁尔科夫神经元为例，给出了一些新结果：（1）给出了能使同步流形存在的拓扑结构，（2）讨论了不同参数变化时同步的稳定性，（3）分析了控制参数、比率以及耦合强度和西格蒙德函数大小的作用。最后，对于两个不同神经元之间的化学耦合，给出了横向系统并分析了两种耦合强度对同步的影响。
