A note on nonautonomous logistic equation with random perturbation
type: Item
instance of: scholarly article
title: A note on nonautonomous logistic equation with random perturbation
zbMATH Open document ID: 1076.34062
author: Daqing Jiang
author: Ning-Zhong Shi
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: Consider the nonautonomous extension of randomized logistic equation \[ dN(t) = N(t) [(a(t)-b(t) N(t)) dt + \alpha (t) dB(t)], \quad N(0)=N_0 > 0,\;t \geq 0, \] driven by a \(1\)-dimensional Brownian motion \(B\) on a probability space \((\Omega,{\mathcal F},({\mathcal F}_t)_{t \geq 0}, P)\). Suppose that the coefficients \(a, b, \alpha\) are continuous, \(T\)-periodic functions satisfying \[ a(t) > 0, \quad b(t) > 0, \quad \int^T_0 [a(s)-\alpha^2(s)] \,ds > 0 . \] This note shows that \(E [1/N(t)]\) has a unique positive \(T\)-periodic solution under these conditions as a natural extension of a well-known property of the underlying deterministic model.
reviewed by: Henri Schurz
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2141748
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: nonautonomous logistic equation
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: periodic solutions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.08.027
OpenAlex ID: W2079337490
cites work: Q4003237
cites work: Volterra integral and differential equations
cites work: Environmental Brownian noise suppresses explosions in population dynamics.
cites work: Q4086525
cites work: Global Models of Growth and Competition
DOI: 10.1016/J.JMAA.2004.08.027
description: scientific article; zbMATH DE number 2141748