This article deals with a model of signal propagation in excitable media based on a system of reaction-diffusion equations. Such media have the ability to exhibit a large response in reaction to a small deviation from the rest state. An example of such media is the nerve tissue or the heart tissue. The first part of the article briefly describes the origin and the propagation of the cardiac action potential in the heart. In the second part, the mathematical properties of the model are discussed. Next, the numerical algorithm based on the finite difference method is used to obtain computational studies in both a homogeneous and heterogeneous medium with an emphasis on interactions of the propagating signals with obstacles in the medium.

中文翻译：

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可激发介质中信号传播的数学模型

本文讨论了基于反应扩散方程组的信号在可激发介质中传播的模型。这样的介质具有对静止状态的微小偏差做出反应的能力。这种介质的一个例子是神经组织或心脏组织。本文的第一部分简要介绍了心脏动作电位在心脏中的起源和传播。在第二部分中，讨论了模型的数学性质。接下来，基于有限差分法的数值算法用于在均质和非均质介质中进行计算研究，重点是传播信号与介质中障碍物的相互作用。