Dynamics of a stochastic Holling II one-predator two-prey system with jumps

Zhang, Xinhong; Li, Wenxue; Liu, Meng; Ke, Wang

doi:10.1016/j.physa.2014.11.060

Cited by 53 publications

(20 citation statements)

References 31 publications

(51 reference statements)

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“…They proved that the system is strongly persistent in mean. Zhang [21] studied dynamics of a stochastic Holling II one-predator two-prey system with jumps. Liu [22] and Ji [23] also investigated the effect of environment on dynamical behaviors of stochastic models.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of a stochastic ratio-dependent predator-prey system with Holling type IV functional response

Fu¹,

Jiang²,

Shi³

et al. 2018

Filomat

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In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predatorprey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and Itô's formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.

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Section: Introductionmentioning

confidence: 99%

Dynamical behavior of a stochastic ratio-dependent predator-prey system with Holling type IV functional response

Fu¹,

Jiang²,

Shi³

et al. 2018

Filomat

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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%

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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“…However, in the real world population systems often suffer sudden environmental perturbations, such as earthquakes, hurricanes, planting, harvesting, etc (see e.g. [9][10][11][12]). These phenomena cannot be described by white noise [13].…”

Section: Introductionmentioning

confidence: 99%

Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic model with Markovian switching and Lévy noise

Wang

Wei

2017

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In this paper, stochastic permanence and extinction of a stochastic logistic model with Markovian switching and Lévy noise are investigated by combining stochastic analytical techniques with M-matrix analysis. Sufficient and necessary conditions of stochastic permanence and extinction are obtained. In the case of stochastic permanence, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the logistic model. Finally, our conclusions are illustrated through an example.

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Dynamics of a stochastic Holling II one-predator two-prey system with jumps

Cited by 53 publications

References 31 publications

Dynamical behavior of a stochastic ratio-dependent predator-prey system with Holling type IV functional response

Dynamical behavior of a stochastic ratio-dependent predator-prey system with Holling type IV functional response

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

Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic model with Markovian switching and Lévy noise

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