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.

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 Permanence and Extinction of a Stochastic Delay Logistic Model with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chun Lu ◽  
Xiaohua Ding
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Population Model ◽  
Logistic Model ◽  
Necessary Conditions ◽  
Biological Significance ◽  
Jump Process ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Sufficient And Necessary Conditions

This paper is concerned with a stochastic delay logistic model with jumps. Sufficient and necessary conditions for extinction are obtained as well as stochastic permanence. Numerical simulations are introduced to support the theoretical analysis results. The results show that the jump process can affect the properties of the population model significantly, which conforms to biological significance.

scholarly journals Survival Analysis of a Nonautonomous Logistic Model with Stochastic Perturbation

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Chun Lu ◽  
Xiaohua Ding
Keyword(s):  
Survival Analysis ◽  
Asymptotic Stability ◽  
White Noise ◽  
Global Asymptotic Stability ◽  
Logistic Model ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Stochastic Permanence ◽  
The Mean

Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence, and global asymptotic stability are established. Moreover, the threshold between weak persistence and extinction is obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.

scholarly journals Stochastic Lotka-Volterra systems under regime switching with jumps

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1907-1928 ◽  
Author(s):  
Ruihua Wu ◽  
Xiaoling Zou ◽  
Ke Wang ◽  
Meng Liu
Keyword(s):  
Markov Chain ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
Stochastic Permanence ◽  
Color Noise ◽  
Volterra Systems ◽  
The Moment

A stochastic Lotka-Volterra model with Markovian switching driven by jumps is proposed and investigated. In the model, the white noise, color noise and jumping noise are taken into account at the same time. This model is more feasible and applicable. Firstly, sufficient conditions for stochastic permanence and extinction are presented. Then the moment average in time and the asymptotic pathwise properties are estimated. Our results show that these properties have close relations with the jumps and the stationary probability distribution of the Markov chain. Finally, several numerical simulations are provided to illustrate the effectiveness of the results.

scholarly journals Dynamics of a stochastic Gilpin–Ayala population model with Markovian switching and impulsive perturbations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuan Jiang ◽  
Zijian Liu ◽  
Jin Yang ◽  
Yuanshun Tan
Keyword(s):  
Regime Switching ◽  
Population Model ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Critical Number ◽  
Stochastic Permanence ◽  
The Mean ◽  
Impulsive Perturbations

Abstract In this paper, we consider the dynamics of a stochastic Gilpin–Ayala model with regime switching and impulsive perturbations. The Gilpin–Ayala parameter is also allowed to switch. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, and stochastic permanence are provided. The critical number among the extinction, nonpersistence in the mean, and weak persistence is obtained. Our results demonstrate that the dynamics of the model have close relations with the impulses and the Markov switching.

scholarly journals Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Li Zu ◽  
Daqing Jiang ◽  
Donal O’Regan
Keyword(s):  
Numerical Simulation ◽  
Stationary Distribution ◽  
Nonlinear Diffusion ◽  
Logistic Model ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Single Species ◽  
Unique Positive Solution ◽  
Stochastic Perturbations ◽  
Stochastic Permanence

We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion amongnpatches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation.

scholarly journals Survival analysis of a stochastic delay single-species system in polluted environment with psychological effect and pulse toxicant input

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiangjun Dai ◽  
Suli Wang ◽  
Weizhi Xiong ◽  
Ni Li
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Threshold Value ◽  
Psychological Effect ◽  
Polluted Environment ◽  
Population System ◽  
Stochastic Delay ◽  
Species Population ◽  
The Mean ◽  
Single Species Population

Abstract We propose and study a stochastic delay single-species population system in polluted environment with psychological effect and pulse toxicant input. We establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and strong persistence of the single-species population and obtain the threshold value between extinction and weak persistence. Finally, we confirm the efficiency of the main results by numerical simulations.

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

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