A dynamical variable driven by the combination of a deterministic multiplicative process with stochastic reset events develops, at long times, a stationary power-law distribution. Here, we analyze how such distribution changes when several variables of the same kind interact with each other through diffusion-like coupling. While for weak coupling the variables are still distributed following power-law functions, their distributions are severely distorted as interactions become stronger, with sudden appearance of cutoffs and divergent singularities. We explore these effects both analytically and numerically, for coupled ensembles of identical and non-identical variables. The most relevant consequences of ensemble heterogeneity are assessed, and preliminary results for spatially distributed ensembles are presented.

由确定性乘法过程与随机重置事件的组合驱动的动态变量在很长一段时间内会形成平稳的幂律分布。在这里，我们分析了当几个同类变量通过类扩散耦合相互作用时，这种分布是如何变化的。虽然对于弱耦合，变量仍然遵循幂律函数分布，但随着相互作用的增强，它们的分布会严重扭曲，突然出现截止点和发散奇点。对于相同和不同变量的耦合集合，我们从分析和数值上探讨了这些影响。评估了集合异质性的最相关后果，并呈现了空间分布集合的初步结果。