The Microscopic Dynamics of a Spatial Ecological Model

Yuri V. Kozitskij, Yuri G. Kondratiev

Publication date: 27 July 2015

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.

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Ecology (92D40) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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