Langford系统Hopf分岔极限环幅值控制

Amplitude control of limit cycle from Hopf bifurcation in the Langford system

系统地研究了Langford系统Hopf分岔极限环幅值非线性反馈控制问题.根据中心流形定理和规范型降维理论,推导含控制增益项的非线性曲率系数控制公式和幅值近似解,通过数值仿真验证并绘制极限环幅控关系曲线.所推导的控制公式为Langford系统极限环幅值控制提供了方便有效的控制方法.

The control of amplitude of limit cycle emerging from the Hopf bifurcation in Langford system under a nonlinear feedback controller is investigate in this paper. Explicit nonlinear control formulae and amplitude approximations in terms of control gains are derived by utilizing the center manifold theory and normal form reduction. Gain-amplitude curves for controlled systems are drawn and verified by numerical simulations. The formulae and expressions for the Langford system present a convenient approach to obtaining an effective analytical control in this system.