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Existence, uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation
Author(s) -
Ji Chunyan,
Jiang Daqing,
Shi Ningzhong,
O'Regan Donal
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.778
Subject(s) - mathematics , uniqueness , logistic function , brownian motion , stochastic differential equation , mathematical analysis , perturbation (astronomy) , initial value problem , stability (learning theory) , statistics , physics , quantum mechanics , machine learning , computer science
This paper discusses a randomized logistic equationwith initial value x (0)= x 0 >0, where B ( t ) is a standard one‐dimension Brownian motion, and θ∈(0, 0.5). We show that the positive solution of the stochastic differential equation does not explode at any finite time under certain conditions. In addition, we study the existence, uniqueness, boundedness, stochastic persistence and global stability of the positive solution. Copyright © 2006 John Wiley & Sons, Ltd.