Hopf bifurcation for delayed neuron equation with arbitrary activation function
Zhou Shangbo①; Liao Xiaofeng②; Yu Juebang①
①Dept. of Opto-electronic Technology UEST of China Chengdu 610054 China;②Faculty of Computer Sci. and Eng., Chongqing University Chongqing 400044 China
Abstract：In this paper, a neural equation with discrete time delay is studied, The transcendental equation corresponding to the above-mentioned linearized system is analyzed. The linear stability for this model has been investigated. For the case with inhibitory influence from the past state, it is found that Hopf bifurcation occurs when this influence varies and passes through a sequence of critical values. The stability of bifurcating periodic solutions and the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Some numerical examples illustrated those results.
2002, Vol. 24 
