一个新系统Hopf分岔极限环幅值控制

Amplitude Control of Limit Cycle from Hopf Bifurcation in a New System

本文研究了一个新的非线性动力系统的Hopf分岔极限环幅值的控制问题.基于非线性动力系统的分岔控制理论,自主设计了一个具有普遍意义的非线性控制器.对应本系统应用具体的非线性控制器实现了Hopf分岔极限环幅值的反馈控制,同时得到了计算极限环幅值近似值的计算公式,最后数值模拟验证了本文理论分析的正确性及控制方法的有效性.

In this paper, we study the amplitude control problem of limit cycle of Hopf bifurcation in a new nonlinear dynamical system. Based on the bifurcation control theory of nonlinear dynamic systems, a universal nonlinear controller is designed. By applying a specific nonlinear controller to the system, we succeed in feedbacking controlling amplitudes of limit cycle of the Hopf bifurcation. We also get the computational formula for approximately calculating amplitudes of the limit cycle. Finally, a series of numerical simulations verify the correctness of the theoretical analysis and the effectiveness of the proposed control method.