✦ LIBER ✦
Existence, uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation
✍ Scribed by Chunyan Ji; Daqing Jiang; Ningzhong Shi; Donal O'Regan
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 128 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.778
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✦ Synopsis
Abstract
This paper discusses a randomized logistic equation
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with 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.