Relaxation oscillation and attractive basins of a two-neuron Hopfield network with slow and fast variables
Yuanguang Zheng, Zaihua Wang
Abstract: In this paper, the nonlinear dynamics of a two-neuron Hopfield network with slow and fast variables is investigated. By means of the geometric singular perturbation theory, the condition that ensures the existence of the relaxation oscillation is obtained, the period of the relaxation oscillation is determined analytically, and the shape of attractive basin of every stable equilibrium is figured out. By using the method of stability switches, the delay effect on the characteristics of the relaxation oscillation and the attractive basins is studied. Case studies are given to demonstrate the validity of theoretical analysis.
原文链接: https://link.springer.com/article/10.1007/s11071-012-0527-7
