【摘要】 Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法,它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性.在一定条件下,Melnikov方法还可以用来研究非线性系统的次谐波分支.文中利用该方法研究了一类PLL方程,证明了该系统次谐波及Smale马蹄意义下的混沌的存在性,并给出了混沌区域及次谐波分支区域.更多还原

【Abstract】 Melnikov method is an effectively mathematical method which is usually used to prove the existence of chaos in the sense of Smale horseshoes.By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map,it is shown whether the system has transversally homoclinicpoints and chaos in the sense of Smale horseshoes.Under the certain conditions,it can also be used to study the subharmonic bifurcations of some nonlinear systems.In this paper,by using the method,a family of PLL equations are studied to show the existence of subharmonic solutions and chaos in the sense of Smale horseshoes.The regions of chaos and subharmonic bifurcations are given.更多还原