Chaotic vibration of the one-dimensional linear wave equation with a van der Pol nonlinear boundary condition  

作　　者：GuogangLIU YiZHAO 

机构地区：[1]DepartmentofMathematics,ZhongshanUniversity,GuangzhouGuangdong510275,China

出　　处：《控制理论与应用（英文版）》2004年第4期358-364,共7页

基　　金：It was supported in part by the National Natural Foundation of China (No. 10371136) and the Guangdong Natural Science Foundation of Guangdong Province (No.021765,031603)

摘　　要：The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations. It characterizes the nonisotropic chaotic vibration by means of the total variation theory. Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations. It characterizes the nonisotropic chaotic vibration by means of the total variation theory. Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.

关 键 词：CHAOS Wave equation Van der Pol nonlinearity Total variation Homoclinic point Topological transitivity 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]