Stability and Hopf bifurcation of the simplified Lang-Kobayashi equation

Abstract

Stability and Hopf bifurcation of the simplified Lang-Kobayashi equation is considered. The critical time delay associated with Hopf bifurcation of the zero equilibrium is determined by applying the bifurcation theorem. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem. Finally, numerical simulations are performed to verify the analytical prediction.