Existence,uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation |
| |
| Authors: | Chunyan Ji Daqing Jiang Ningzhong Shi Donal O'Regan |
| |
| Institution: | 1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, People's Republic of China;2. Department of Mathematics, Changshu Institute of Technology, Changshu 215500, Jiangsu, People's Republic of China;3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, People's Republic of ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, People's Republic of China===;4. Department of Mathematics, National University of Ireland, Galway, Ireland |
| |
| Abstract: | This paper discusses a randomized logistic equation ![equation image]( "equation image") (1) with initial value x(0)=x0>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. |
| |
| Keywords: | Itô 's formula global stability Lyapunov function existence uniqueness persistence boundedness Brownian motion |
|
|
