一类简化Lang-Kobayashi方程的Hopf分岔及其稳定性

讨论了一类简化Lang-Kobayashi方程的Hopf 分岔的性质.根据分岔理论，给出了系统产生Hopf 分岔的临界时滞条件，然后利用中心流形定理和规范型理论得到了确定Hopf分岔方向和分岔周期解的稳定性计算公式.最后，用数值模拟对理论结果进行了验证.关键词：Lang-Kobayashi方程时滞Hopf分岔稳定性

Stability and Hopf bifurcation of the simplified Lang-Kobayashi equation

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.