一个多态系统的混合吸引域和开关阵发

INTERMINGLED BASINS AND ON-OFF INTERMITTENCY OF A MULTI-STATE SYSTEM

提出了一个具有无穷多低维对称不变子空间的多态系统，用以描述受阻尼力和周期力影响并在二维势中运动的粒子，以此研究多态的混合吸引域和开关阵发现象．在每一个子空间中均有一个混饨吸引子，此外相空间中没有别的吸引子，当某个系统参数改变时，对于不变子空间的最大横截李雅普诺夫指数从负值变为正值，系统动力学行为相应从混合吸引域态变为多态的开关阵发态．

A dynamical system is considered, which contains infinite low-dimensional symmetric invariant subspaces and describes a partile moving in a two-dimensional potential subjected to friction and periodic forcing to investigate intermingled basins and on-off intermittency of multi-state. There is a Chaotic attractor in each subepace, and no other attractors in the phase space. As a parathe of the sysetem changes, the largest Lyapunov exponent transverse to the invariant subspaces can change from negative to positive, then the system dynamics changes from intermingled basin state to a multi-state on- off intermittency.Statistical behvior of the intermittency states is also investigated.