Stochastic model of population growth and spread
type: Item
instance of: scholarly article
title: Stochastic model of population growth and spread
zbMATH Open document ID: 0617.92017
DOI: 10.1007/BF02459957
author: S. S. De
published in: Bulletin of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: A stochastic model for the population regulated by logistic growth and spreading in a given region of two- or three-dimensional space has been introduced. For many-species population the interactions among the species have also been incorporated in this model. From the random variables that describe stochastic processes of Wiener type the space-dependent random population densities have been formed and shown to satisfy the Langevin equations. The Fokker-Planck equation corresponding to these Langevin equations has been approximately solved for the transition probability of the population spreading and it has been found that such approximate expressions of the transition probability depend on the solutions of the deterministic equations of the diffusion model with logistic growth and interaction. Also, the stationary or equilibrium solutions of the Fokker-Planck equation together with the special discussion on the pattern of single- species population spreading have been made.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 4001934
zbMATH Keywords: logistic growth
zbMATH Keywords: spreading
zbMATH Keywords: many-species population
zbMATH Keywords: interactions
zbMATH Keywords: stochastic processes of Wiener type
zbMATH Keywords: space-dependent random population densities
zbMATH Keywords: Langevin equations
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: approximate expressions of the transition probability
zbMATH Keywords: diffusion model
zbMATH Keywords: equilibrium solutions
MaRDI profile type: Publication
Wikidata QID: Q69118161
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full work available at URL: https://doi.org/10.1007/bf02459957
OpenAlex ID: W4247785096
description: scientific article; zbMATH DE number 4001934