中文摘要：

为了研究倒摆系统的全局动力学行为,利用Mel’nikov方法研究了一类倒摆系统的混沌运动,给出了划分系统混沌运动与非混沌运动的参数临界曲线。利用Runge-Kutta方法对系统进行数值模拟,给出了系统的相图和庞加莱截面图,验证了理论分析的结果。结果表明：系统存在由于同宿轨道的稳定流形与不稳定流形横截相交而产生的Smale马蹄意义下的混沌;随着激励频率的增加,混沌阈值先增大、后减小。

英文摘要：

To study the global dynamics of the inverted pendulum system,chaotic motions for a class of the inverted pendulum system were investigated with Mel＇nikov method.The critical curves seperating the chaotic and non-chaotic regions of the system were presented.Using the Runge-Kutta method,numerical simulations including the phase portaits and the Poincarésections were given,which verified the analytical results.Results show that there exists Smale horseshoe chaos arising from transversal intersections of stable and unstable manifold of the homoclinic orbit;the critical values for chaos first increase and then decrease as the increasing of the excitation frequency.