Lyapunov functions for a generalized Gause-type model

Ardito, A.; Ricciardi, P.

doi:10.1007/bf00187283

Cited by 41 publications

(24 citation statements)

References 15 publications

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“…In this paper we shall restrict our attentions to the global stability of the equilibrium which represents the extinction of top-predator. We prove the main result by extending the Lyapunov functions introduced by A. Ardito and P. Ricciardi [1]. We discuss the problem for general three species food chain models, in particular, the case of the Holling's type III functional response.…”

Section: ) X(t) Y(t) and Z(t)mentioning

confidence: 83%

Extinction of top-predator in a three-level food-chain model

Chiu

Hsu²

1998

Journal of Mathematical Biology

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Abstract. In this paper we extend the Lyapunov functions, constructed by A. Ardito and P. Ricciardi for predator-prey system [1], to the three level food chain models. We first consider a general three-level food-chain model. A criterion for the extinction of top predator will be given. Then we restrict our attentions to the case in which the prey is of logistic growth and predators have Holling's type II functional responses.

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Section: ) X(t) Y(t) and Z(t)mentioning

confidence: 83%

Extinction of top-predator in a three-level food-chain model

Chiu

Hsu²

1998

Journal of Mathematical Biology

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“…For (k − 1)/2 < λ < k − 1, a Lyapunov functional is known for ODE in (2.36) [2], but it cannot be generalized to the R-D system case [21].…”

Section: Hopf Bifurcation In Diffusive Predator-prey Systemmentioning

confidence: 98%

“…2) In the remaining part of this article, we focus on the system (1.2). For the new parameters, k is a rescaled carrying capacity; θ is the death rate of the predator, and m is the strength of the interaction.…”

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confidence: 99%

Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system

Wei

Shi

2009

Journal of Differential Equations

483

330

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A diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered. Hopf and steady state bifurcation analysis are carried out in details. In particular we show the existence of multiple spatially non-homogeneous periodic orbits while the system parameters are all spatially homogeneous. Our results and global bifurcation theory also suggest the existence of loops of spatially non-homogeneous periodic orbits and steady state solutions. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation.

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“…Adapting an argument from Ardito and Ricciardi [8] (they consider a logistic-type resource rather than a donor-controlled one), let…”

Section: Appendix Global Asymptotic Stability Of Positive Equilibriumentioning

confidence: 99%

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

Nevai

Gorder

2012

Journal of Biological Dynamics

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The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.

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Lyapunov functions for a generalized Gause-type model

Cited by 41 publications

References 15 publications

Extinction of top-predator in a three-level food-chain model

Extinction of top-predator in a three-level food-chain model

Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

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