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arXiv · 2003.09313

Infinite populations of migrants as complex systems: self-regulation

Yuri Kozitsky
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Abstract

A model is proposed and studied describing an infinite population of point migrants arriving in and departing from $X\subseteq \mathbf{R}^d$, $d\geq 1$. Both these acts occur at random with state-dependent rates. That is, depending on their geometry the existing migrants repel and attract the newcomers, which makes the population a complex system. Its states are probability measures on an appropriate configuration space, and their evolution $\mu_0 \to \mu_t$ is obtained by solving the corresponding Fokker-Planck equation. The main result is the conclusion that this evolution of states preserves their sub-Poissonicity, and hence a local self-regulation (suppression of clustering) takes place due to the inter-particle repulsion -- no matter of how small range. Further possibilities to study the proposed model with the help of this result are also discussed.

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Yuri Kozitsky. 2020-03-20. Infinite populations of migrants as complex systems: self-regulation. https://arxiv.org/abs/2003.09313

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