关键词: 时滞, Hopf分岔, 周期解, 全局存在性

Abstract: We studied the existence of periodic solutions of a neural network with time delay. We firstly investigated the local stability of the system and deduced the conditions of a local Hopf bifurcation. Moreover, using the global Hopf bifurcation theorem for FDE, we also obtained the conditions that guarantee the neuron has multiple periodic solutions.

Key words: time delay, Hopf bifurcation, periodic solutions, global existence