Stability and Bifurcation Behavior of a Neuron System with Hyper-Strong Kernel

At present, there are few studies on the delayed kernel function of hyper-strong kernel. This paper attempts to analyze the stability and bifurcation of neural networks with distributed delayed hyper-strong kernels. Firstly, considering the average delay as a bifurcation parameter, the study discusses the characteristic equations of delayed kernels with weak kernel, strong kernel and hyper-strong kernel to provide sufficient conditions for the stability and generation of Hopf bifurcation. Secondly, it applies the normal theory and the center manifold theory to derive the formulas for determining the stability and direction of the bifurcating periodic solution. Finally, it verifies the correctness of the calculation results by numerical simulation with an example.

Automated summary

This paper analyzes the stability and bifurcation of neural networks with distributed delayed hyper-strong kernels. It provides conditions for stability and Hopf bifurcation by discussing the characteristic equations of delayed kernels with different strengths. The study uses normal theory and center manifold theory to determine the stability and direction of bifurcating periodic solutions, and verifies the results through numerical simulation.