Global existence of periodic solutions in a simplified four‐neuron BAM neural network model with multiple delays
Xiang‐Ping Yan, Wan‐Tong Li · Discrete Dynamics in Nature and Society · 2006
We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson′s criterion for high‐dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.