Hopf Bifurcation Analysis of KdV–Burgers–Kuramoto Chaotic System with Distributed Delay Feedback

Abstract

In this paper, the KdV–Burgers–Kuramoto chaotic system with distributed delay feedback is studied. The local stability of equilibrium points of this system is analyzed and the conditions under which Hopf bifurcation occurs are obtained by choosing the mean time delay as a bifurcation parameter. The direction and stability of bifurcating periodic solutions are derived by means of the normal form theory and the center manifold theorem. Numerical simulations are also illustrated which are in agreement with our theoretical results.