STABILITY AND HOPF BIFURCATION ON A TWO-NEURON SYSTEM WITH TIME DELAY IN THE FREQUENCY DOMAIN
Wenwu Yu, Jinde Cao · International Journal of Bifurcation and Chaos · 2007
In this paper, a general two-neuron model with time delay is considered, where the time delay is regarded as a parameter. It is found that Hopf bifurcation occurs when this delay passes through a sequence of critical value. By analyzing the characteristic equation and using the frequency domain approach, the existence of Hopf bifurcation is determined. The stability of bifurcating periodic solutions are determined by the harmonic balance approach, Nyquist criterion and the graphic Hopf bifurcation theorem. Numerical results are given to justify the theoretical analysis.