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arXiv · 1507.07517

The Microscopic Dynamics of a Spatial Ecological Model

Yuri Kondratiev·Yuri Kozitsky
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Abstract

The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes a competition term. The system's states are probability measures on the space of configurations of entities, and their evolution is described by means of a hierarchical chain of equations for the corresponding correlation functions derived from the Fokker-Planck equation for measures. Under natural conditions imposed on the model parameters it is proved that the correlation functions evolve in a scale of Banach spaces in such a way that each correlation function corresponds to a unique sub-Poissonian state. Some further properties of the evolution of states constructed in this way are also described.

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Yuri Kondratiev, Yuri Kozitsky. 2015-12-19. The Microscopic Dynamics of a Spatial Ecological Model. https://arxiv.org/abs/1507.07517

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