【摘要】 针对二自由度周期激励下的复数Duffing振荡系统 ,讨论了系统的不动点、奇怪吸引子和混沌控制问题 ;应用Pyragas方法对复数Duffing振荡系统混沌进行控制 ,提出了一种非线性控制方法 ;推导了控制输入的函数表示 ,并针对不同的控制输入参数进行了数值计算 .数值结果表明 ,同传统的混沌控制法相比较 ,该方法具有控制过程简单、控制时间短的特点 ,并且通过选择合适的控制输入参数 ,可以有效地控制Duffing系统的混沌 ,使系统达到期望的稳定目标点和目标轨道 ,具有重要的实际应用价值更多还原

【Abstract】 Aiming at the periodically forced complex Duffing’s oscillation system of two degrees of freedom, the fixed point, strange attractors and chaotic control of the system are studied. The problem of chaos control for this oscillaion system is studied by using the method introduced by Pyragas, and a function of controlling input is deduced. The controlling function and desired result of chaos control are presented through theoretical analysis with nonlinear ideas. The theoretical and numerical results indicate that this method reveals shorter controlling time and simpler controlling process compared with the traditional chaos control method. The trajectories of chaotic system can be controlled to approach the target points and periodic orbits through adjusting the input function, so this new method has an actual application to the control of this system.更多还原