Abstract The dynamics is studied of an infinite continuum system of jumping and coalescing point particles. In the course of jumps, the particles repel each other whereas their coalescence is free. Such models have multiple applications, e.g., in the theory of evolving ecological systems. As the equation of motion we take a kinetic equation, derived by a scaling procedure from the microscopic Fokker-Planck equation corresponding to this kind of motion. This procedure – as well as some general interconnections between the micro- and mesocopic descriptions of such systems – are also discussed. The main result of the paper is the numerical study (by the Runge-Kutta method) of the solutions of the kinetic equation revealing a number of interesting peculiarities of the dynamics and clarifying the particular role of the jumps and the coalescence in the system’s evolution. Possible nontrivial stationary states are also found and analyzed.

中文翻译：

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连续体中的跳跃和合并：一项数值研究

摘要 研究了一个无限连续系统的跳跃和聚结点粒子的动力学。在跳跃过程中，粒子相互排斥，而它们的聚结是自由的。这种模型有多种应用，例如，在进化生态系统的理论中。我们采用一个动力学方程作为运动方程，它是从对应于这种运动的微观 Fokker-Planck 方程中通过缩放程序导出的。还讨论了该程序以及此类系统的微观和中观描述之间的一些一般互连。该论文的主要结果是对动力学方程解的数值研究（通过 Runge-Kutta 方法）揭示了动力学的许多有趣特性，并阐明了跳跃和合并在系统演化中的特殊作用。还发现并分析了可能的非平凡平稳状态。