An invariant measure for a system of stochastic equations for a prey-predator model with spatial diffusion
type: Item
instance of: scholarly article
title: An invariant measure for a system of stochastic equations for a prey-predator model with spatial diffusion
zbMATH Open document ID: 1241.92073
DOI: 10.4171/RSMUP/124-4
author: Saliha Hamdous
author: Luigi Manca
author: Hisao Fujita Yashima
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2011-02-10T00:00:00Z
full work available at URL: https://eudml.org/doc/243361
full work available at URL: http://rendiconti.math.unipd.it/volumes/vol124.php
review text: This paper considers a stochastic prey-predator model with spatial diffusion in a Hilbert abstract space: \[ dN_1(t) = [(\alpha - \beta N_2(t) - \mu N_1(t))N_1(t) + \kappa_1 \Delta N_1(t)]dt + \rho_1 N_1(t)dW(t), \] \[ dN_2(t) = [(-\gamma + \delta N_1(t) - \nu N_2(t))N_2(t) + \kappa_2 \Delta N_2(t)]dt + \rho_2 N_2(t)dW(t). \] Here, \(N_1\) and \(N_2\) are the population densities of the two species, \(\alpha,\;\beta,\;\gamma,\;\delta,\;\mu,\;\nu,\;\rho_i\) and \(\kappa_i\) are some positive constants and \(W(t)\) is a Brownian motion. The authors prove the existence of an invariant measure for this system of stochastic equations. The proof of this result is based on a theorem of Krylov-Bogoliubov and estimation of the solution.
reviewed by: Iulian Stoleriu
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 5849495
zbMATH Keywords: invariant measure
zbMATH Keywords: stochastic differential system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5849495