Permanence of a stochastic prey–predator model with a general functional response

Li, Shangzhi; Guo, Shangjiang

doi:10.1016/j.matcom.2021.02.025

Cited by 15 publications

(8 citation statements)

References 23 publications

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“…It is worth mentioning that although we have analyzed the influences of environmental heterogeneity and population movement on disease transmission, there are still other factors worth considering, such as stochastic perturbation [27,28,29], the periodic incidence rate, saturated treatment rate, advection [5,6,46], nonlocal dispersal [10], and boundary conditions [13,15,44]. We leave these as future research.…”

Section: Discussionmentioning

confidence: 99%

Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment

Tian¹,

Guo²,

Liu³

2021

DCDS-B

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<p style='text-indent:20px;'>This paper is devoted to an SEIR epidemic model with variable recruitment and both exposed and infected populations having infectious in a spatially heterogeneous environment. The basic reproduction number is defined and the existence of endemic equilibrium is obtained, and the relationship between the basic reproduction number and diffusion coefficients is established. Then the global stability of the endemic equilibrium in a homogeneous environment is investigated. Finally, the asymptotic profiles of endemic equilibrium are discussed, when the diffusion rates of susceptible, exposed and infected individuals tend to zero or infinity. The theoretical results show that limiting the movement of exposed, infected and recovered individuals can eliminate the disease in low-risk sites, while the disease is still persistent in high-risk sites. Therefore, the presence of exposed individuals with infectious greatly increases the difficulty of disease prevention and control.</p>

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Section: Discussionmentioning

confidence: 99%

Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment

Tian¹,

Guo²,

Liu³

2021

DCDS-B

Self Cite

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“…Under

N=2,{r}_1>0

and

{r}_2<0

, a specified case of (2) is the stochastic prey–predator model with Holling type II, which has been investigated in other studies (Li, 2022; Liu et al, 2016; Lv et al, 2018; Lv & Wang, 2011). In particular, Li and Guo (2021) examined the permanence of a stochastic prey–predator model featuring a general functional response. This model introduced intrinsic growth rate and intraspecific interaction rate noises, expanding the former from the intrinsic growth rate noise to encompass both intrinsic growth rate and intraspecific interaction rate noises.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behaviour of a non‐autonomous multispecies Holling type II model with a complex type of noises

Xu,

Ma,

Zhao

2024

Stat

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The deterministic non‐autonomous multispecies Holling type II model and its stochastic version with a simple type of noise have been proposed to infer multispecies community structure. However, these models fail to account for complex types of noises, which may render the model overly simplistic. In this paper, a non‐autonomous multispecies Holling type II model with a complex type of noise has been proposed. We establish sufficient conditions for various mathematical properties of the solutions, including existence and uniqueness, stochastic permanence and extinction. Additionally, numerical simulation studies are provided to illustrate our theoretical findings.

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“…Ren and Shi [2] dealt with the global boundedness and stability of solutions of a predator-prey system with time delay. Li and Guo [3] introduced a new way to study the permanence and extinction for a stochastic prey-predator system involving functional response. Alsakaji et al [4] made a detailed discussion on permanence, local and global stabilities, Hopf bifurcation, and a predatorprey model with time delay.…”

Section: Introductionmentioning

confidence: 99%

“…Here we notice that the works of [1][2][3][4][5][6][7][8] are concerned with the integer-order predator-prey models. In recent years, fractional-order dynamical systems have found potential application in numerous areas such as all sorts of physical waves, neural network systems, biological technique, finance, automatic control, and so on [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

Yao

Tang

2021

Discrete Dynamics in Nature and Society

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In the present work, we mainly focus on a new established fractional-order predator-prey system concerning both types of time delays. Exploiting an advisable change of variable, we set up an isovalent fractional-order predator-prey model concerning a single delay. Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. The numerical simulation figures and bifurcation plots successfully support the correctness of the established key conclusions.

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Permanence of a stochastic prey–predator model with a general functional response

Cited by 15 publications

References 23 publications

Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment

Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment

Asymptotic behaviour of a non‐autonomous multispecies Holling type II model with a complex type of noises

Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

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