Global stability of a periodic Holling‐Tanner predator‐prey model

Lisena, Benedetta

doi:10.1002/mma.4814

Cited by 11 publications

(9 citation statements)

References 12 publications

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“…As a consequence of Theorem 2.1, we get the existence of a positive T -periodic solution to system (2.3). In fact, the following result (see [5]) holds true.…”

Section: Preliminary Resultsmentioning

confidence: 84%

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Diffusive Holling–Tanner predator–prey models in periodic environments

Montano

Lisena

2019

Applied Mathematics Letters

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“…As a consequence of Theorem 2.1, we get the existence of a positive T -periodic solution to system (2.3). In fact, the following result (see [5]) holds true.…”

Section: Preliminary Resultsmentioning

confidence: 84%

“…Let us recall some recent results concerning ODE Holling-Tanner predator-prey models with periodic coefficients (see [5]).…”

Section: Preliminary Resultsmentioning

confidence: 99%

Diffusive Holling–Tanner predator–prey models in periodic environments

Montano

Lisena

2019

Applied Mathematics Letters

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“…The authors also found that there is always one positive equilibrium point in the first quadrant which can be stable; unstable surrounded by a stable limit cycle; or stable surrounded by two limit cycles. Additionally, the global stability of a periodic solution of this predator-prey model was investigated by [30] and the analysis of a discrete May-Holling-Tanner model was described in [12].…”

Section: Introductionmentioning

confidence: 99%

A modified May–Holling–Tanner predator-prey model with multiple Allee effects on the prey and an alternative food source for the predator

Arancibia–Ibarra¹,

Flores²,

Bode³

et al. 2021

Discrete &Amp; Continuous Dynamical Systems - B

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In the present study, we have modified the traditional May-Holling-Tanner predator-prey model used to represent the interaction between least weasel and field-vole population by adding an Allee effect (strong and weak) on the field-vole population and alternative food source for the weasel population. It is shown that the dynamic is different from the original May-Holling-Tanner predator-prey interaction since new equilibrium points have appeared in the first quadrant. Moreover, the modified model allows the extinction of both species when the Allee effect (strong and weak) on the prey is included, while the inclusion of the alternative food source for the predator shows that the system can support the coexistence of the populations, extinction of the prey and coexistence and oscillation of the populations at the same time. Furthermore, we use numerical simulations to illustrate the impact that changing the predation rate and the predator intrinsic growth rate have on the basin of attraction of the stable equilibrium point or stable limit cycle in the first quadrant. These simulations show the stabilisation of predator and prey populations and/or the oscillation of these two species over time.

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“…The dynamics of two‐species predator–prey systems has been widely studied (see, e.g., previous studies 1–10 ). However, the investigation of one prey–two predators systems seems to exhibit much richer characteristics (see previous studies 11‐19 ).…”

Section: Introductionmentioning

confidence: 99%

A diffusive two predators–one prey model on periodically evolving domains

Montano

Lisena

2021

Math Methods in App Sciences

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The paper deals with a diffusive two predators–one prey model with Holling‐type II functional response. We assume that the density of prey and predators is spatially inhomogeneous on a periodically evolving domain and is subject to homogeneous Neumann boundary conditions. We focus on the case in which all populations have periodic logistic growth, if isolated, and no competition occurs between predators. Our main purpose is to study the asymptotic properties of the solutions of this reaction–diffusion model. More specifically, suitable conditions, depending on the domain evolution function and the space dimension, are introduced leading to the extinction of one predator and the stable coexistence of the surviving predator and its prey. Their density, as time tends to infinity, tends to the periodic solution of the corresponding kinetic predator–prey model. Finally, the autonomous model on a fixed domain is treated.

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Global stability of a periodic Holling‐Tanner predator‐prey model

Cited by 11 publications

References 12 publications

Diffusive Holling–Tanner predator–prey models in periodic environments

Diffusive Holling–Tanner predator–prey models in periodic environments

A modified May–Holling–Tanner predator-prey model with multiple Allee effects on the prey and an alternative food source for the predator

A diffusive two predators–one prey model on periodically evolving domains

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