For distributed evolutionary dynamical systems of the “reaction-diffusion” and “reaction-diffusion-advection” types, we analyze the behavior of invariant numerical characteristics of the attractor as the diffusion coefficients decrease. We consider the phenomenon of multimode diffusion chaos, one of whose signatures is an increase in the Lyapunov dimensions of the attractor. For several examples, we perform broad numerical experiments illustrating this phenomenon.

中文翻译：

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扩散混沌及其不变的数值特征

对于“反应-扩散”和“反应-扩散-平流”类型的分布式演化动力系统，我们分析了随着扩散系数的减小吸引子的不变数值特性的行为。我们考虑多模扩散混沌现象，其特征之一是吸引子的李雅普诺夫维数增加。对于几个例子，我们进行了广泛的数值实验来说明这种现象。