On stochastic Gilpin–Ayala population model with Markovian switching

Settati, Adel; Lahrouz, Aadil

doi:10.1016/j.biosystems.2015.01.004

Cited by 30 publications

(17 citation statements)

References 29 publications

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“…Thus, for any given positive constant K, there exists a sufficient large N 0 such that [15] we obtain the first part of the theorem. Now we prove the second part.…”

Section: Stationary Distributionmentioning

confidence: 72%

“…i) For all i ∈ S, σ 2 (i) = 0, then model (5) reduces to model (3), and the condition θ(i) + 1 2γ(i) for each i ∈ S can be removed, then we get the same result as that in Settati et. al (2015) [15].…”

Section: Stationary Distributionmentioning

confidence: 99%

“…The contribution of this paper is that. Compared with the models in the literatures(e.g., [2,[7][8][9][10][11]15]), our model (5) Throughout this paper, we assume that there is a complete probability space (Ω, F ,…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic properties of a stochastic Gilpin–Ayala model under regime switching

Wang

Zhu

2019

Nonlinear Analysis: Hybrid Systems

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In this paper, a stochastic Gilpin-Ayala population model with regime switching and white noise is considered. All parameters are influenced by stochastic perturbations. The existence of global positive solution, asymptotic stability in probability, pth moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model are investigated, which generalize some results in the literatures. Moreover, the conditions presented for the stochastic permanence and the existence of stationary distribution improve the previous results.

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“…Thus, for any given positive constant K, there exists a sufficient large N 0 such that [15] we obtain the first part of the theorem. Now we prove the second part.…”

Section: Stationary Distributionmentioning

confidence: 72%

Section: Stationary Distributionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic properties of a stochastic Gilpin–Ayala model under regime switching

Wang

Zhu

2019

Nonlinear Analysis: Hybrid Systems

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“…Construct Lyapunov functional W(t) = e μt V 1 (t) + V 2 (t). Applying Equations (20) and (30), we have…”

Section: Global Exponential Stabilitymentioning

confidence: 99%

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays

Zhao

2018

Journal of Biological Dynamics

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In this paper, we study the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.

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“…The nonlinear item and the regime-switching mechanism exist in the model simultaneously, which might make the problem more complicated (see e.g. [18,19], and [17] for more details). Based on this motivation, our aim is to tackle this issue.…”

Section: Introductionmentioning

confidence: 99%

Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching

Liu

Zhu

2017

Adv Differ Equ

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We are interested in the persistence in mean and extinction for a stochastic competitive Gilpin-Ayala system with regime switching. Based on the stochastic LaSalle theorem and the space-decomposition method, we derive generalized sufficient criteria on persistence in mean and extinction. By constructing a novel Lyapunov function we establish sufficient criteria on partial persistence in mean and partial extinction for the system. Finally, we provide two examples to demonstrate the feasibility and validity of our proposed methods.

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On stochastic Gilpin–Ayala population model with Markovian switching

Cited by 30 publications

References 29 publications

Asymptotic properties of a stochastic Gilpin–Ayala model under regime switching

Asymptotic properties of a stochastic Gilpin–Ayala model under regime switching

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays

Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching

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