Dynamics of a Discrete Prey–Predator Model with Mixed Functional Response

Elettreby, M. F.; Khawagi, Aisha; Nabil, Tamer

doi:10.1142/s0218127419501992

Cited by 20 publications

(9 citation statements)

References 35 publications

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“…Predator-prey systems with mixed functional and numerical responses have been used in a few studies to describe some kinds of environment, which study the dynamic behaviors of these models such as [28][29][30]. Te authors of [28] used the Holling type II and Beddington-DeAngelis type as mixed functional responses to investigate the stability and fnd out the persistence condition; while in [29], they used the Holling type IV and Holling type I as mixed functional responses to examine the local and global stability and obtain the persistence condition.…”

Section: Introductionmentioning

confidence: 99%

“…Te authors of [28] used the Holling type II and Beddington-DeAngelis type as mixed functional responses to investigate the stability and fnd out the persistence condition; while in [29], they used the Holling type IV and Holling type I as mixed functional responses to examine the local and global stability and obtain the persistence condition. Finally, in [30], the authors investigated the stability of the equilibrium points of a discrete Lotka-Volterra predator-prey model with mixed functional responses of Holling type I and II, and the model was studied in terms of its long-term behavior when each control parameter was changed.…”

Section: Introductionmentioning

confidence: 99%

“…With the values of parameters, the equilibrium point E 1 (k, 0) is represented by E 1 (4, 0), which has two cases as proved theoretically in Teorem 3, in Figure 1, it is observed that E 1 (4, 0) is stable, as it heads towards the point E 1 (4, 0), because condition ( 30) is satisfed in Teorem 3. However, if the value of the death rate of the predator (s) is changed, then condition (30) is not satisfed and point E 1 (4, 0) becomes a saddle point (i.e., an unstable case) as shown in Figure 2, where the stream of arrows is moving away from the point E 1 (4, 0). (1 + ξX ...…”

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confidence: 99%

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Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Alebraheem

2023

Journal of Mathematics

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Predator interference refers to the competition effect on individuals of the same species through preventing or limiting access to a resource. In this paper, a novel predator–prey model that includes predator interference is considered. In the novel model, a high prey density is taken into consideration by investigating Crowley–Martin as a numerical response, while the growth rate of prey is logistically described and Holling type II is used as a functional response. In contrast to literature, this model has distinct and notable features: predator and prey species have an intraspecific competition, and this model has a numerical response that generalizes several of the commonly utilized depictions of predator interference. The boundedness of the model is proved. Predator interference effects are theoretically and numerically studied in terms of stability, coexistence, and extinction. Theoretical results show that the system has no effect on coexistence or extinction in these types of models. Numerical simulations present two different dynamics with identical results on the theoretical side of model stabilization for both dynamics. Moreover, the numerical simulations show that there is a change from periodic to steady state dynamics as the value of predator interference increases. This means that the coexistence probability of the model increases. The attained results are explained from both a mathematical and an ecological points of view.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Alebraheem

2023

Journal of Mathematics

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“…Roy et al [16] proposed a class of prey-predator model consisting of prey, predator and generalist predator, and incorporated Holling type II and III functional responses into different prey-predator interaction. The dynamics of discrete prey-predator model with Holling type I and II functional responses were discussed in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional three-species food chain system with mixed functional responses and fear effect

Wang

Alsaedi²,

Huang

2023

Preprint

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In this paper, a novel fractional three-species food chain system with Ivlev-type and ratio-dependent functional responses is proposed. Also the fear effect of the middle predator on the prey is taken into account. First the boundedness of the solutions and the existence of positive equilibrium point are investigated for the non-delayed system, and then the delay-induced Hopf bifurcation is dealt with for the delayed system via feedback control method. Some sufficient Hopf bifurcation conditions are obtained based on Hopf bifurcation theorem and stability theorem for fractional dynamical systems. A simulation example is given to support our theoretical results, and especially the effect of the feedback gains and the level of fear on the stability and bifurcation behavior are discussed by illustrations.

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“…Liu and Cai [31] explored the presence of bifurcation and chaos in a discretetime prey-predator system. Elettreby et al [32] used mixed functional response to investigate the dynamics of a discrete prey-predator model. AlSharawi et al [33] studied a discrete prey-predator model with a nonmonotonic functional response and strong Allee effect in prey.…”

Section: Introductionmentioning

confidence: 99%

Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete‐Time Prey‐Predator Model

Mahapatra¹,

Santra

Bonyah³

2021

Complexity

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Prey-predator models with refuge effect have great importance in the context of ecology. Constant refuge and refuge proportional to prey are the most popular concepts of refuge in the existing literature. Now, there are new different types of refuge concepts attracting researchers. This study considers a refuge concept proportional to the predator due to the fear induced by predators. When predators increase, fears also increase and that is why prey refuges also increase. Here, we examine the influence of prey refuge proportional to predator effect in a discrete prey-predator interaction with the Holling type II functional response model. Is this refuge stabilizing or destabilizing the system? That is the central question of this study. The existence and stability of fixed points, Period-Doubling Bifurcation, Neimark–Sacker Bifurcation, the influence of prey refuge, and chaos are analyzed. This work provides the bifurcation diagrams and Lyapunov exponents to analyze the refuge parameter of the model. The proposed discrete model indicates rich dynamics as the effect of prey refuge through numerical simulations.

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Dynamics of a Discrete Prey–Predator Model with Mixed Functional Response

Cited by 20 publications

References 35 publications

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Dynamics of a fractional three-species food chain system with mixed functional responses and fear effect

Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete‐Time Prey‐Predator Model

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