Izue, Yukishige (Hokkaido Univ.), Enomoto, Ryuji (Toba National Coll. of Maritime Tech.), Yamashita, Yuh (Hokkaido Univ.)

Numerical Computation of Dissipative Boundaries for Two-Dimensional Gradient-Like Morse-Smale Dynamical Systems

Scheduled for presentation during the Regular Session "Nonlinear Control II" (ThP05), Thursday, July 27, 2006, 16:35−17:00, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

This paper is concerned with a method to construct the Lyapunov function in the sense of Conley for an arbitrary two-dimensional gradient-like Morse-Smale dynamical system with global compact attractors. The dynamical system is allowed to have singular points. In our approach, we compute some characteristic dissipative boundaries (the level surface of the Lyapunov function) of finite number and then use them to construct the Lyapunov function. This paper describes the algorithm for computing a dissipative boundary numerically and discusses the prospects for using the dissipative boundaries to construct the Lyapunov function.