This paper is concerned with chaotification of first-order partial difference equations. Two criteria of chaos for the difference equations with general controllers are established, and all the controlled systems are proved to be chaotic in the sense of Li–Yorke or of both Li–Yorke and Devaney by applying the coupled-expanding theory of general discrete dynamical systems. The controllers used in this paper can be easily constructed, facilitating the chaotification of first-order partial difference equations. For illustration, two illustrative examples are provided.

中文翻译：

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一阶偏微分方程的混沌化

本文关注一阶偏微分方程的混沌化。建立了具有一般控制器的差分方程的两个混沌判据，并应用一般离散动力学耦合扩展理论证明了所有受控系统在Li-Yorke或Li-Yorke和Devaney意义上都是混沌的。系统。本文使用的控制器可以很容易地构造，有利于一阶偏微分方程的混乱化。为了说明，提供了两个说明性示例。