A mathematical model of single population dispersal

The mathematical model is based on the variant of species population settlement in different but close habitats. It is assumed that the dynamics of the population community in a particular habitat depends on its properties and internal regulatory mechanisms. That is, fertility and mortality are determined by a trophic resource, while migration of individuals to neighboring habitats is determined by the search for a trophic resource or by sociogenic factors. Resettlement is considered as a random movement of some individuals from the “maternal” zone into neighboring habitats. The model is represented by a Cauchy problem for a system of ordinary differential equations connected by a matrix of “transitions”. The logistic equation is taken as the basis of the model of population dynamics of a single population. All parameters and characteristics of zones are chosen randomly from a given range. Numerical implementation of the solutions is carried out in the programming environment of the mathematical package Matlab with the use of vectorization of calculations.