一类Silnikov方程的Hopf分岔控制

摘要

研究一类Silnikov方程的Hopf分岔现象。从理论上推导出受控系统发生Hopf分岔的条件，得到Hopf分岔的方向和周期解的稳定性。通过设计非线性控制器实现了对系统极限环幅值的控制，通过数值模拟验证了本文提出的控制方法的有效性。%Hopf bifurcation of a class of Silnikov equation is studied in the paper. The condition that Hopf bi-furcation occurs for the controlled system is derived theoretically. The direction of Hopf bifurcation and the sta-bility of the periodic solutions are obtained. The control of amplitude of the limit cycle is established by the nonlinear controller. The validity of the control method proposed in the paper is verified by the numerical simu-lation.