By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its period...By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10672193)
文摘By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.
