Dynamics of non-autonomous stochastic Gilpin–Ayala competition model with time-varying delays

Jovanović, Miljana; Vasilova, Maja

doi:10.1016/j.amc.2012.12.073

Cited by 16 publications

(9 citation statements)

References 28 publications

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“…In recent years, stochastic versions Gilpin-Ayala model have been studied by many authors. We mention some of the works (Jiang et al, 2008;Jiang and Shi, 2005;Jovanovic and Vasilova, 2013;Hu, 2006, 2008;Liu and Wang, 2012;Li, 2013;Vasilova and Jovanovic, 2011;Vasilova, 2013) and the references therein. Jiang et al (2008) and Jiang and Shi (2005) considered the following non-autonomous randomized model based on (2):…”

Section: Q3mentioning

confidence: 99%

On stochastic Gilpin–Ayala population model with Markovian switching

Settati¹,

Lahrouz²

2015

Biosystems

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Section: Q3mentioning

confidence: 99%

On stochastic Gilpin–Ayala population model with Markovian switching

Settati¹,

Lahrouz²

2015

Biosystems

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“…Cushing [5] studies the LotkaVolterra equations for two competing species under the assumption that the coefficients are periodic functions of a common period. Linear assumptions in Lotka-Volterra models for the interspecific interference are relaxed in GilpinAyala models, recently analyzed by Jovanović and Vasilova [11,19]. In the case of some models of two species competing in a randomly varying environment, Ellner [6] obtains sufficient conditions for convergence to the corresponding stationary distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In a more general setting, we may cite the work by Cushing [5], Ellner [6], Gopalsamy [9], Jovanović and Vasilova [11,19], Li and Smith [12,13], Qi-Min et al [15], and Zhang and Han [20], among others, who study a variety of models under stochastic and deterministic perspectives, such as age-dependent mortality and fertility functions (Gopalsamy [9]), age-structured models (Qi-Min et al [15], Zhang and Han [20]), and four species that coexist in competition for three essential resources (Li and Smith [12]). Cushing [5] studies the LotkaVolterra equations for two competing species under the assumption that the coefficients are periodic functions of a common period.…”

Section: Introductionmentioning

confidence: 99%

Lifetime and reproduction of a marked individual in a two-species competition process

Gómez‐Corral

López‐García

2015

Applied Mathematics and Computation

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The interest is in a stochastic model for the competition of two species, which was first introduced by Reuter [16] and Iglehart [10], and then analyzed by . The model is related to the two-species autonomous competitive model (Zeeman [21]), where individuals compete either directly or indirectly for a limited food supply and, consequently, births and death rates depend on the population sizes of one or both of the species. The aim is to complement the treatment of the model we started in [7,8] by focusing here on probabilistic descriptors that are inherently linked to an individual: its residual lifetime and the number of direct descendants. We present an approximating model based on the maximum size distribution, and we discuss on various models defined in terms of the underlying killing and reproductive strategies. Numerical examples are presented to show the effects of the killing and reproductive strategies on the behavior of an individual, and how the impact of these strategies on the descriptors vanishes in highly competitive ecosystems.

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“…In essence, random factors can lead to complete extinction of populations even if the population size is relatively large. Previous studies have explored the dynamic properties for stochastic single species models [14][15][16], stochastic predator-prey models [17][18][19][20][21][22][23], stochastic competitive models [24][25][26][27], stochastic mutualism model [28][29][30][31]. Specially, Liu and Wang [32] investigated a two-prey one-predator model with random perturbations.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Stochastic Intraguild Predation Model

2016

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Intraguild predation (IGP) is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.

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Dynamics of non-autonomous stochastic Gilpin–Ayala competition model with time-varying delays

Cited by 16 publications

References 28 publications

On stochastic Gilpin–Ayala population model with Markovian switching

On stochastic Gilpin–Ayala population model with Markovian switching

Lifetime and reproduction of a marked individual in a two-species competition process

Dynamics of a Stochastic Intraguild Predation Model

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