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

The publication delves into the dynamic characteristics of neuron systems with hyper-strong kernels, a topic that has received less attention compared to weak and strong kernels. It analyzes the stability and bifurcation behaviors of these systems, highlighting the significant impact of kernel types on the system's critical value. The research also explores how the number of neurons affects the stability of weak kernel systems, providing a deeper understanding of the complex dynamics in neural networks. The study employs advanced mathematical techniques, including the normal form and central manifold theory, to derive formulas for determining the direction and stability of Hopf bifurcations. Numerical simulations validate the theoretical findings, offering a compelling case for further exploration into the intricate behaviors of neuron systems with distributed delays.