Jumps and coalescence in the continuum: A numerical study

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.