Zero-Hopf bifurcation analysis in an inertial two-neural system with delayed Crespi function

In this paper, we study a four-dimensional inertial two-nervous system with delay. By analyzing the distribution of eigenvalues, the critical value of zero-Hopf bifurcation is obtained. Complex dynamic behaviors are considered when two parameters change simultaneously. Pitchfork and Hopf bifurcation critical lines at near the zero-Hopf point are obtained by using the central manifold reduction and the normal form theory. The bifurcation diagram is given, and the results of period-doubling bifurcation into chaotic region in the inertial two-neural system with delayed Crespi function are shown.