scholarly journals Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Rensheng He ◽  
Zuoliang Xiong ◽  
Desheng Hong
Keyword(s):  
Lyapunov Functions ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Matrix Analysis ◽  
Stationary Probability ◽  
Functional Responses ◽  
Stationary Probability Distribution ◽  
Stochastic Permanence ◽  
Prey Model ◽  
Telegraph Noise

We propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By theM-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent on the subsystems’ parameters and the stationary probability distribution of the Markov chain. We also investigate another asymptotic property and finally give two examples and numerical simulations to illustrate 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 Dynamical Behaviors of Stochastic Delayed One-Predator and Two-Competing-Prey Systems with Holling Type IV and Crowley-Martin Type Functional Responses

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Changjian Wang ◽  
Zuoliang Xiong ◽  
Rensheng He ◽  
Hongwei Yin
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Functional Responses ◽  
Stochastic Permanence ◽  
Numerical Examples ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
Stochastic Boundedness ◽  
Globally Positive Solution

This paper is devoted to stochastic delayed one-predator and two-competing-prey systems with two kinds of different functional responses. By establishing appropriate Lyapunov functions, the globally positive solution and stochastic boundedness are investigated. In some case, the stochastic permanence and extinction are also obtained. Moreover, sufficient conditions of the global asymptotic stability of the system are established. Finally, some numerical examples are provided to explain our conclusions.

scholarly journals Dynamics of a stochastic HIV/AIDS model with treatment under regime switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Stationary Distribution ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Aids Model ◽  
Telegraph Noise ◽  
Spread Dynamics ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Hiv Aids

<p style='text-indent:20px;'>This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.</p>

Stationary distribution and extinction for a stochastic two-compartment model of B-cell chronic lymphocytic leukemia

2021 ◽  
pp. 2150065
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Xiangdan Wen
Keyword(s):  
Chronic Lymphocytic Leukemia ◽  
Stationary Distribution ◽  
Lyapunov Functions ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Compartment Model ◽  
Lymphocytic Leukemia ◽  
Two Compartment Model ◽  
Theoretical Results ◽  
Cell Chronic Lymphocytic Leukemia

In this paper, we study the dynamical behavior of a stochastic two-compartment model of [Formula: see text]-cell chronic lymphocytic leukemia, which is perturbed by white noise. Firstly, by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then, conditions for extinction of the disease are derived. Furthermore, numerical simulations are presented for supporting the theoretical results. Our results show that large noise intensity may contribute to extinction of the disease.

Mixing properties of harris chains and autoregressive processes

1986 ◽  
Vol 23 (4) ◽  
pp. 880-892 ◽  
Author(s):  
Krishna B. Athreya ◽  
Sastry G. Pantula
Keyword(s):  
Sufficient Conditions ◽  
Autoregressive Process ◽  
Strong Mixing ◽  
Stationary Probability ◽  
Autoregressive Processes ◽  
Stationary Probability Distribution ◽  
Mixing Properties ◽  
Recurrent Markov Chain ◽  
General State Space ◽  
Necessary And Sufficient

Let {Yn: n ≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn} is strong mixing, provided there exists a stationary probability distribution π (·) for {Yn}. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.

scholarly journals Dynamics in a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Azhar Halik ◽  
Hong-Li Li
Keyword(s):  
Time Delays ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Comparison Method ◽  
Cooperative System ◽  
Functional Responses ◽  
Feedback Controls ◽  
Lyapunov Function Method ◽  
Inequality Techniques ◽  
Ratio Dependent

AbstractThis study investigates the dynamical behavior of a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays. Compared with previous studies, both ratio-dependent functional responses and time delays are considered. By employing the comparison method, the Lyapunov function method, and useful inequality techniques, some sufficient conditions on the permanence, periodic solution, and global attractivity for the considered system are derived. Finally, a numerical example is also presented to validate the practicability and feasibility of our proposed results.

Mixing properties of harris chains and autoregressive processes

1986 ◽  
Vol 23 (04) ◽  
pp. 880-892 ◽  
Author(s):  
Krishna B. Athreya ◽  
Sastry G. Pantula
Keyword(s):  
Sufficient Conditions ◽  
Autoregressive Process ◽  
Strong Mixing ◽  
Stationary Probability ◽  
Autoregressive Processes ◽  
Stationary Probability Distribution ◽  
Mixing Properties ◽  
Recurrent Markov Chain ◽  
General State Space ◽  
Necessary And Sufficient

Let {Yn:n≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn} is strong mixing, provided there exists a stationary probability distributionπ(·) for {Yn}. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.

scholarly journals Dynamics Analysis of a Stochastic Leslie–Gower Predator-Prey Model with Feedback Controls

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Huailan Ren ◽  
Wencai Zhao
Keyword(s):  
Lyapunov Functions ◽  
Type Ii ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Noise Interference ◽  
Predator Prey Model ◽  
Prey Model ◽  
Global Positive Solution ◽  
Theoretical Results

This study focuses on the investigation of a stochastic Leslie–Gower predator-prey model with feedback controls and Holling type II functional responses. First, the existence and uniqueness of a global positive solution to the system under white noise interference are proved. Second, the conditions for the existence of the system’s positive recurrence are established by constructing suitable Lyapunov functions. Additionally, the persistence and extinction of prey and predator in the system are discussed, and the impacts of noise interference and feedback controls on the system are revealed. Finally, we validate the theoretical results by numerical simulations.

The Permanence of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

2013 ◽  
Vol 765-767 ◽  
pp. 327-330
Author(s):  
Chang You Wang ◽  
Xiang Wei Li ◽  
Hong Yuan
Keyword(s):  
Feedback Control ◽  
Sufficient Conditions ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Analysis Technique ◽  
Ratio Dependent

This paper is concerned with a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls. By developing a new analysis technique, we establish the sufficient conditions which guarantee the permanence of the model.

scholarly journals Global Stability for a Predator-Prey Model with Dispersal among Patches

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Gao ◽  
Shengqiang Liu
Keyword(s):  
Global Stability ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Graph Theoretical Approach

We investigate a predator-prey model with dispersal for both predator and prey amongnpatches; our main purpose is to extend the global stability criteria by Li and Shuai (2010) on a predator-prey model with dispersal for prey amongnpatches. By using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, we derive sufficient conditions under which the positive coexistence equilibrium of this model is unique and globally asymptotically stable if it exists.

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