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

Montano, Mirella Cappelletti; Lisena, Benedetta

doi:10.1002/mma.7323

Cited by 3 publications

(3 citation statements)

References 28 publications

(36 reference statements)

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“…However, for more complex cases, numerical studies may be necessary. For instance, the evolution of many species to ecosystem conditions with eutrophication and complex environment [18]- [20] and chaos phenomena [21] serve as an example. Despite its drawbacks, this method provides an in-depth look at the capabilities of logistic equations with their variations as one of the fundamental processes in nature.…”

Section: (15)mentioning

confidence: 99%

Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Salim¹,

Sulaiman²,

Kenji³

2023

J. Multidiscip. Appl. Nat. Sci.

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The present study aims to obtain an analytic solution for the inhomogeneous Verhults equation using multiple expansion methods. This study identifies the external factors represented by the inhomogeneous term that determine optimal variable conditions for ecosystem population growth. The simulation involves scenarios that utilize constant growth rates, periodic growth rates, constant external factors, and periodic external factors. It is found that external factors increase population growth, whereas constant external factors prevent growth under saturation conditions. Periodic external factors cause fluctuations in the amplitude of growth regions. The present study will highlight and discuss the development and application of the solution.

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Section: (15)mentioning

confidence: 99%

Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Salim¹,

Sulaiman²,

Kenji³

2023

J. Multidiscip. Appl. Nat. Sci.

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“…(17). To highlight the dependence of N(θ), P(θ) and Q on δ 3 , we designate these by N(δ 3 ; µ), P(δ 3 ; θ) and Q(δ 3 ; X) respectively, where P(X) is defined by (12). The proof of the result below is similar to a result in [30] and the proof is not given here.…”

Section: Non-constant Solution Through Bifurcationmentioning

confidence: 99%

“…The two predator-one prey model can be found in [11]. Recently, Mirella Cappelletti and Lisena [12] analyzed the impact of diffusion on a single prey and two predator system. They studied the asymptotic properties of the solutions of the model.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a diffusive two predators- one prey system

Mukherjee

2023

Electron. J. Appl. Math.

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This paper analyses a diffusive predator-prey model consisting of a single prey species and two predator species with modified Leslie-Gower term Holling type II functional response subject to the homogeneous Neumann boundary condition. Local stability condition is derived by the application of Routh-Hurwitz criterion. Global asymptotic stability of the unique positive steady state is shown by constructing a suitable Lyapunov function when self diffusion is allowed where as non-constant positive steady states can exist due to the presence of cross-diffusion, that means, cross-diffusion can induce stationary pattern. Taking the cross diffusion as a bifurcation parameter, one can show the existence of positive non-constant solutions with the help of bifurcation theory. A brief conclusion completes the paper.

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Threshold dynamics scenario of a plants-pollinators cooperative system with impulsive effect on a periodically evolving domain

Wang,

Yang,

Wang

et al. 2024

Eur. J. Appl. Math

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Flowering plants depend on some animals for pollination and contribute to nourish the animals in natural environments. We call these animals pollinators and build a plants-pollinators cooperative model with impulsive effect on a periodically evolving domain. Next, we define the ecological reproduction index for single plant model and plants-pollinators system, respectively, whose threshold dynamics, including the extinction, persistence and coexistence, is established by the method of upper and lower solutions. Theoretical analysis shows that a large domain evolution rate has a positive influence on the survival of pollinators whether or not the impulsive effect occurs, and the pulse eliminates the pollinators even when the evolution rate is high. Moreover, some selective numerical simulations are still performed to explain our theoretical results.

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

Cited by 3 publications

References 28 publications

Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Dynamics of a diffusive two predators- one prey system

Threshold dynamics scenario of a plants-pollinators cooperative system with impulsive effect on a periodically evolving domain

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