Hopf bifurcation of traveling wave solutions of delayed Fisher-KPP equation

The dynamical behavior of the traveling wave front solutions of the delayed Fisher-KPP equation is studied by employing the theory of functional differential equation. It is found that, when the delay term τ comes through a threshold, one equilibrium point is always unstable and there exists a periodic solution near the other equilibrium point in the traveling wave equation. By using the theory of center manifold and normal form, the stability of the bifurcating periodic solution, which corresponds to the periodic traveling wave solution of the original equation, is obtained. Finally, some numerical simulations are also given to illustrate our results of theoretical analysis.