Asymptotic properties and simulations of a stochastic logistic model under regime switching

Liu, Meng; Wang, Ke

doi:10.1016/j.mcm.2011.05.023

Cited by 45 publications

(35 citation statements)

References 29 publications

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“…If lim sup t→∞ t −1 0<t k <t ln(1 + b k ) = 0, then our result is consistent with [22,Theorem 2]. It reveals that the small impulse has no nature impact on the species, but from the result we can see that the negative impulse can contribute on the extinction of the population and the positive impulse can resist the extinction of species, this also coincides with the reality.…”

Section: Definition 32 ([13]supporting

confidence: 89%

“…By simple computation, we see h(r(t)) = 0.6 − 0.4 > 0, by the results of [22], the species will be weakly persistent, in Figure 1 Now we take the impulse into account, in Example 5.1, let b k = e −0.6 − 1, t k = k be negative impulses, then the result changes greatly. By computation, we have lim sup t→∞ t −1 0<t k <t ln(1 + b k ) + h(r(t)) = −0.4 < 0, then species x(t) will be extinct.…”

Section: Numerical Simulationsmentioning

confidence: 92%

“…The stochastic Gilpin-Ayala models have been studied a lot, the readers can refer to [12,13,19,22,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of stochastic hybrid Gilpin-Ayala system with impulsive perturbations

Wu¹

2017

J. Nonlinear Sci. Appl.

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This paper is mainly concerned with the dynamics of the stochastic Gilpin-Ayala model under regime switching with impulsive perturbations. The goal is to analyze the effects of Markov chain and impulse on the dynamics. Some asymptotic properties are considered and sufficient criteria for stochastic permanence, extinction, non-persistence in the mean and weak persistence are obtained. The critical value among the extinction, non-persistence in the mean and weak persistence is explored. Our results demonstrate that the dynamics of the model have close relations with the impulse and the stationary distribution of the Markov chain.

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Section: Definition 32 ([13]supporting

confidence: 89%

Section: Numerical Simulationsmentioning

confidence: 92%

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Dynamics of stochastic hybrid Gilpin-Ayala system with impulsive perturbations

Wu¹

2017

J. Nonlinear Sci. Appl.

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“…The noise has important effects on the model: Mao et al [23] showed that the environmental Brownian noise suppresses explosion in population dynamics. There are many other papers in the literature on models with white noise; readers can refer to [11,17,13,18,14,19,20] and the references cited therein.…”

Section: The Classical Nonautonomous Logistic Equation Is Dx(t) = X(tmentioning

confidence: 99%

Population dynamical behaviors of stochastic logistic system with jumps

Wu¹,

Ke²

2014

Turk J Math

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This paper is concerned with a stochastic logistic model driven by martingales with jumps. In the model, generalized noise and jump noise are taken into account. This model is new and more feasible. The explicit global positive solution of the system is presented, and then sufficient conditions for extinction and persistence are established.The critical value of extinction, nonpersistence in the mean, and weak persistence in the mean are obtained. The pathwise and moment properties are also investigated. Finally, some simulation figures are introduced to illustrate the main results.

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“…May [20] also noted that due to environmental fluctuation, birth rates, carrying capacity, competition coefficients and other parameters involved in a population model system exhibit random fluctuation to a greater or lesser extent. Therefore, many authors introduced stochastic perturbations into the deterministic models [16,19,29,33]. Takeuchi et al [28] considered the following predator-prey model with telegraph noise based on model (1.1):…”

Section: Introductionmentioning

confidence: 99%

The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey

Li¹,

Zhang²

2017

J. Nonlinear Sci. Appl.

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In this paper, a class of predator-prey model with prey competition is proposed, in which the interactions of predation between predator and prey are randomised and subsequently evaluated under Markovian switching. By constructing appropriate Lyapunov functions and applying various analytical methods, sufficient conditions for the existence of unique global positive solution, stochastic permanence and mean extinction are established. In the permanence case, we also estimate the superior and inferior limits of the sample path in a time-averaged Markov decision. We conclude that the interactions between predator and two prey, two competitive prey themselves and the dynamical properties of switching subsystems are not only dependent on subsystem coefficients but also on the transition probability of the Markov chain (switching from one state to another). Specific examples and numerical simulations are provided to demonstrate our theoretical results.

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Asymptotic properties and simulations of a stochastic logistic model under regime switching

Cited by 45 publications

References 29 publications

Dynamics of stochastic hybrid Gilpin-Ayala system with impulsive perturbations

Dynamics of stochastic hybrid Gilpin-Ayala system with impulsive perturbations

Population dynamical behaviors of stochastic logistic system with jumps

The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey

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