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.

偏微分方程（PDE）系统混沌动力学的研究已成为动力学系统的研究重点。尽管一维波PDE混沌理论的研究取得了重要进展，但对二维（2D）双曲PDE混沌振动的理解仍然不完整。本文涉及二维双曲PDE系统，该系统由具有两个超线性边界条件的线性方程控制。基于混沌映射理论和特征方法，在三个不同的系统参数下，获得了存在各向同性混沌振动的充分条件。此外，提供了三个数值示例来说明我们的理论结果的有效性。