Stochastic Lotka–Volterra systems with Lévy noise

Liu, Meng; Wang, K e

doi:10.1016/j.jmaa.2013.07.078

Cited by 153 publications

(73 citation statements)

References 17 publications

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“…The proofs of the existence and uniqueness of the global positive solution and (3.1) are similar to these in [22] (Lemmas 3 and 4), and hence are omitted. The proof of (3.2) is similar to that in [2] (Theorem 3.1) and we omit it too.…”

Section: Persistence and Extinctionmentioning

confidence: 99%

Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting

Wang¹,

Du²,

Liu³

2017

J. Nonlinear Sci. Appl.

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In this paper, we propose a stochastic service-resource mutualism model with Lévy noises and harvesting. Under some assumptions, we study several dynamical properties of the model. We first obtain the thresholds between persistence and extinction for both the service species and the resource species. Then we give sharp sufficient conditions for stability in distribution of the model. Finally, we establish sufficient and necessary criteria for the existence of the optimal harvesting policy. The optimal harvesting effort and maximum of sustainable yield are also obtained. Our results reveal that the persistence, extinction, stability in distribution and optimal harvesting strategy have close relationships with the random noises.

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Section: Persistence and Extinctionmentioning

confidence: 99%

Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting

Wang¹,

Du²,

Liu³

2017

J. Nonlinear Sci. Appl.

Self Cite

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“…Bao et al in [10,11] firstly proposed that these phenomena could be described by Lévy noise. At present, there are many research papers considering Lévy noise [6,[12][13][14][15][16][17]. In this paper, we use white noise and Lévy noise to simulate the random change of environment.…”

Section: Introductionmentioning

confidence: 99%

LG–Holling type II diseased predator ecosystem with Lévy noise and white noise

2018

Adv Differ Equ

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This paper considers an LG-Holling type II diseased predator ecosystem with Lévy noise and white noise. In this prey-predator system, assuming that the predator population is infected by disease and divided into two classes: susceptible predator and infected predator, we show that the system has a unique global positive solution. We investigate the persistence in the mean and extinction for the population, obtain threshold conditions of extinction, persistence in the mean by Itô's formula and a comparison theorem for the stochastic system. In addition, we discuss the uniform boundedness of pth moment with p > 0 and reveal the stochastically ultimate boundedness of the system. Finally, some numerical simulations are introduced to illustrate our analytical findings.

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“…To explain these phenomena, introducing a jump process into the underlying population dynamics is one of the important methods. Thus, there are many scholars introduce Lévy jumps into the population system [27][28][29][30][31]. Taking all above influences into consideration, we focus on the infected stochastic predatorprey system with Lévy jumps and delays in a polluted environment…”

Section: Introductionmentioning

confidence: 99%

“…, and is bounded and continuous with respect to ] and is B(Y ) × F -measurable, and 1 + > 0 ( = 1, 2, 3) (see [27][28][29][30]). Moreover, ( ) ( = 1, 2, 3) are independent of , are death rates of species, and ≥ 0 ( = 1, 2, 3, 4) represent the time delay.…”

Section: Introductionmentioning

confidence: 99%

Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

et al. 2017

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In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

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Stochastic Lotka–Volterra systems with Lévy noise

Cited by 153 publications

References 17 publications

Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting

Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting

LG–Holling type II diseased predator ecosystem with Lévy noise and white noise

Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

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