Chaotic Dynamics of a 2D Hyperbolic PDE with the Boundary Conditions of Superlinear Type

The study of the chaotic dynamics of partial differential equation (PDE) system has become the focus of dynamical system. While important progress has been made for the research of chaos theory of one-dimensional wave PDE, the understanding of chaotic vibrations for two-dimensional (2D) hyperbolic PDE is still incomplete. This paper is concerned with a 2D hyperbolic PDE system governed by a linear equation with two suplinear boundary conditions. Based on the chaotic mapping theory and method of characteristics, sufficient conditions for the existence of nonisotropic chaotic vibrations are obtained for such system under three different system parameters. In addition, three numerical examples are provided to illustrate the effectiveness of our theoretical results.