Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey

Solís, Francisco J.; Kú-Carrillo, Roberto A.

doi:10.1155/2015/241312

Cited by 7 publications

(3 citation statements)

References 21 publications

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“…Therefore, condition (13) guarantees that 𝑊 [𝐷 𝐹(𝐸 , 𝑘 * )(𝑈 , 𝑈 )] ≠ 0. Hence, by Sotomayor's theorem, a transcritical bifurcation takes place.…”

Section: Bifurcation Analysismentioning

confidence: 99%

“…Besides the basic relationship given by the Lotka-Volterra model; many factors may affect species growth. So, this model was developed by many researchers taking into consideration various environmental factors that affect the existence and stability of this system, such as prey refuge [2][3][4], disease [5,6], delay [7], harvesting [7][8][9], Allee effect [4,10,11], age structure [12], sex structure and sexual favoritism [13], seasonal variation [14], and many other factors. The functional response is an essential part of the predator-prey model, which describes the change in prey number killed per individual predator per unit of time as a consequence of changes in prey density.…”

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confidence: 99%

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The Dynamics of Modified Leslie-Gower Predator-Prey Model Under the Influence of Nonlinear Harvesting and Fear Effect

Al-Momen

Naji²

2022

Iraqi Journal of Science

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A modified Leslie-Gower predator-prey model with fear effect and nonlinear harvesting is developed and investigated in this study. The predator is supposed to feed on the prey using Holling type-II functional response. The goal is to see how fear of predation and presence of harvesting affect the model's dynamics. The system's positivity and boundlessness are demonstrated. All conceivable equilibria's existence and stability requirements are established. All sorts of local bifurcation occurrence conditions are presented. Extensive numerical simulations of the proposed model are shown in form of Phase portraits and direction fields. That is to guarantee the correctness of the theoretical results of the dynamic behavior of the system and to confirm the existence of various forms of bifurcations. The fear rate is observed to have a stabilizing effect up to a threshold value, after which it leads to prey extinction. The harvesting coefficients, on the other hand, serve as control parameters that, when exceeded, trigger the system to extinction.

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“…Therefore, condition (13) guarantees that 𝑊 [𝐷 𝐹(𝐸 , 𝑘 * )(𝑈 , 𝑈 )] ≠ 0. Hence, by Sotomayor's theorem, a transcritical bifurcation takes place.…”

Section: Bifurcation Analysismentioning

confidence: 99%

mentioning

confidence: 99%

The Dynamics of Modified Leslie-Gower Predator-Prey Model Under the Influence of Nonlinear Harvesting and Fear Effect

Al-Momen

Naji²

2022

Iraqi Journal of Science

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“…A detailed survey of the current and past mathematical literature on cannibalism shows that various types of predator-prey models have been investigated [6,[10][11][12][13][14][15][16]. Most works in the literature consider cannibalism in the predator species.…”

Section: Introductionmentioning

confidence: 99%

The “Destabilizing” Effect of Cannibalism in a Spatially Explicit Three-Species Age Structured Predator-Prey Model

et al. 2017

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Cannibalism, the act of killing and consumption of conspecifics, is generally considered to be a stabilising process in ODE models of predator-prey systems. On the other hand, Sun et al. were the first to show that cannibalism can cause Turing instability, in the classical Rosenzweig-McArthur two-species PDE model, which is an impossibility without cannibalism. Magnússon’s classic work is the first to show that cannibalism in a structured three-species predator-prey ODE model can actually be destabilising. In the current manuscript we consider the PDE form of the three-species model proposed in Magnússon’s classic work. We prove that, in the absence of cannibalism, Turing instability is an impossibility in this model, forany range of parameters. However, theinclusionof cannibalism can cause Turing instability. Thus, to the best of our knowledge, we report thefirstcannibalism induced Turing instability result, in spatially explicit three-species age structured predator-prey systems. We also show that, in the classical ODE model proposed by Magnússon, cannibalism can act as a life boat mechanism,for the prey.

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Prey cannibalism alters the dynamics of Holling–Tanner-type predator–prey models

et al. 2016

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Abstract. Cannibalism, which is the act of killing and at least partial consumption of conspecifics, is ubiquitous in nature. Mathematical models have considered cannibalism in the predator primarily, and show that predator cannibalism in two species ODE models provides a strong stabilizing effect. There is strong ecological evidence that cannibalism exists among prey as well, yet this phenomenon has been much less investigated. In the current manuscript, we investigate both the ODE and spatially explicit forms of a Holling-Tanner model, with ratio dependent functional response. We show that cannibalism in the predator provides a stabilizing influence as expected. However, when cannibalism in the prey is considered, we show that it cannot stabilise the unstable interior equilibrium in the ODE case, but can destabilise the stable interior equilibrium. In the spatially explicit case, we show that in certain parameter regime, prey cannibalism can lead to pattern forming Turing dynamics, which is an impossibility without it. Lastly we consider a stochastic prey cannibalism rate, and find that it can alter both spatial patterns, as well as limit cycle dynamics.

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Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey

Cited by 7 publications

References 21 publications

The Dynamics of Modified Leslie-Gower Predator-Prey Model Under the Influence of Nonlinear Harvesting and Fear Effect

The Dynamics of Modified Leslie-Gower Predator-Prey Model Under the Influence of Nonlinear Harvesting and Fear Effect

The “Destabilizing” Effect of Cannibalism in a Spatially Explicit Three-Species Age Structured Predator-Prey Model

Prey cannibalism alters the dynamics of Holling–Tanner-type predator–prey models

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