We consider the problem of local dynamics of a system of a diffusive-coupled chain of the Van der Pol equations. A transition to the spatially distributed nonlinear boundary-value problem is performed on the assumption of a large number of elements in the chain. Critical cases in the problem of the equilibrium-state stability are emphasized, and all of them have infinite dimension. An algorithm for reducing the input problem to a study of special nonlinear equations of the parabolic type with one or two spatial variables is developed. The nonlocal dynamics of such equations determines the behavior of all solutions of the input problem in the neighborhood of the equilibrium state.

中文翻译：

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耦合范德波尔方程链的局部动力学

我们考虑范德波尔方程的扩散耦合链系统的局部动力学问题。假设链中有大量元素，可以转换到空间分布的非线性边值问题。强调了平衡态稳定性问题中的临界情况，它们都具有无限维数。开发了一种将输入问题简化为研究具有一个或两个空间变量的抛物线型特殊非线性方程的算法。这种方程的非局部动力学决定了输入问题在平衡状态附近的所有解的行为。