scholarly journals A stochastic delay Gilpin-Ayala competition system under regime switching

Filomat ◽  
2013 ◽  
Vol 27 (6) ◽  
pp. 955-964 ◽  
Author(s):  
Yiliang Liu ◽  
Qun Liu
Keyword(s):  
Regime Switching ◽  
Stochastic Delay ◽  
Competition System

scholarly journals Stochastic Delay Population Dynamics under Regime Switching: Permanence and Asymptotic Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Population Dynamics ◽  
Random Environment ◽  
Regime Switching ◽  
Matrix Method ◽  
Volterra Model ◽  
Function Technique ◽  
Stochastic Delay ◽  
Switching Diffusion ◽  
Asymptotic Estimation ◽  
Diffusion In Random Environment

This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. Permanence and asymptotic estimations of solutions are investigated by virtue of V-function technique, M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

STOCHASTIC DELAY GILPIN–AYALA COMPETITION MODELS

2006 ◽  
Vol 06 (04) ◽  
pp. 561-576 ◽  
Author(s):  
BAOSHENG LIAN ◽  
SHIGENG HU
Keyword(s):  
Environmental Noise ◽  
Stochastic Delay ◽  
Competition System ◽  
Population Explosion ◽  
Competition Models ◽  
Potential Population

In this paper, we investigate a stochastic Gilpin–Ayala competition system, which is more general and more realistic than the classical Lotka–Volterra competition system. We reveal that the environmental noise will not only suppress a potential population explosion in the stochastic delay Gilpin–Ayala competition system but also make the solutions stochastically ultimately bounded. Comparing the classical Lotka–Volterra with Gilpin–Ayala competition system, we find that the latter has better proprieties.

scholarly journals Stochastic Delay Logistic Model under Regime Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Regime Switching ◽  
Logistic Model ◽  
Sufficient Conditions ◽  
Function Technique ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Gronwall’S Inequality ◽  
Diffusion In Random Environment ◽  
Stochastically Ultimate Boundedness ◽  
Generalized Itô Formula

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue ofV-function technique,M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

scholarly journals Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Regime Switching ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Volterra Model ◽  
Ultimate Boundedness ◽  
Stochastic Delay ◽  
Switching Diffusion ◽  
Diffusion In Random Environment ◽  
Stochastically Ultimate Boundedness ◽  
Generalized Itô Formula

This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Finally, an example is given to illustrate the main results.

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