In this paper, chaotic dynamics of a class of partial difference equations are investigated. With the help of the coupled-expansion theory of general discrete dynamical systems, two chaotification schemes for partial difference equations with polynomial maps are established. These controlled equations are proved to be chaotic either in the sense of Li–Yorke or in the sense of both Li–Yorke and Devaney. One example is provided to illustrate the theoretical results with computer simulations for demonstration.

中文翻译：

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具有多项式映射的偏差分方程的混沌动力学

本文研究了一类偏微分方程的混沌动力学。借助一般离散动力系统的耦合展开理论，建立了多项式映射偏微分方程的两种混沌格式。这些受控方程在 Li-Yorke 的意义上或在 Li-Yorke 和 Devaney 的意义上都被证明是混沌的。提供了一个例子来说明理论结果，并通过计算机模拟进行演示。