scholarly journals Persistence and extinction of a stochastic delay competitive system under regime switching

2019 ◽  
Vol 2019 (1) ◽  
Keyword(s):  
Regime Switching ◽  
Competitive System ◽  
Stochastic Delay

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.

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 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 Dynamical Analysis and Optimal Harvesting Strategy for a Stochastic Delayed Predator-Prey Competitive System with Lévy Jumps

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Guodong Liu ◽  
Kaiyuan Liu ◽  
Xinzhu Meng
Keyword(s):  
Hessian Matrix ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Optimal Harvesting ◽  
Competitive System ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Lévy Jumps

This paper develops a theoretical framework to investigate optimal harvesting control for stochastic delay differential systems. We first propose a novel stochastic two-predator and one-prey competitive system subject to time delays and Lévy jumps. Then we obtain sufficient conditions for persistence in mean and extinction of three species by using the stochastic qualitative analysis method. Finally, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of delay differential equations. Moreover, some numerical simulations are given to illustrate the theoretical 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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