Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator

Thirthar, Ashraf Adnan; Majeed, Salam J.; Alqudah, Manar A.; Panja, Prabir; Abdeljawad, Thabet

doi:10.1016/j.chaos.2022.112091

Cited by 39 publications

(10 citation statements)

References 33 publications

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“…Remark 4. The impact of fear effect on the population densities and stability has been discussed through numerical simulations or theoretical analysis in [21][22][23][24][25][26]. To get an insight into the role of fear effect, we adopt the values of parameters in (22) except changing the fear level ρ from ρ = 0.18 to ρ = 0.24, 0.3, 0.43, 0.62 successively with τ 1 = 0.2, τ 2 = 3.3.…”

Section: Simulation Examplementioning

confidence: 99%

“…Also they further verified that the level of fear had a significant effect on the stability and Hopf bifurcation of the relevant predator-prey model. Since then, more and more researchers have considered the fear effect of predators in the dynamical study on prey-predator models [21][22][23][24][25][26]. For instance, Zhang et al [21] investigated the impact of the fear effect on the stability and Hopf bifurcation for a prey-predator model with Holling type II functional response by selecting the level of fear as the bifurcation parameter.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Simulation Examplementioning

confidence: 99%

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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“…Some modifications based on the biological behaviors are integrated to construct a better model. For example, the predator-prey model involving the effect of fear [1][2][3][4], the impact of Allee to the existence of prey and predator [5][6][7][8], and the exploitation of biological resources by harvesting [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Predator-Prey Model with Age Structure on Predator and Nonlinear Harvesting on Prey

Panigoro¹,

Resmawan

Sidik

et al. 2022

Jambura J. Math

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In this manuscript, the dynamics of a fractional-order predator-prey model with age structure on predator and nonlinear harvesting on prey are studied. The Caputo fractional-order derivative is used as the operator of the model by considering its capability to explain the present state as the impact of all of the previous conditions. Three biological equilibrium points are successfully identified including their existing properties. The local dynamical behaviors around each equilibrium point are investigated by utilizing the Matignon condition along with the linearization process. The numerical simulations are demonstrated not only to show the local stability which confirms all of the previous analytical results but also to show the existence of periodic signal as the impact of the occurrence of Hopf bifurcation.

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“…Predator-prey interactions are an important component of biological communities. There are numerous publications [10,11,12,13,14,15,16,17,18,19,20] have been published in order to gain a better understanding of the predator-prey system's dynamics. Fear can be explored using a mathematical model in predator-prey interactions, which is becoming a hot topic in ecology and theoretical biology.…”

Section: Introductionmentioning

confidence: 99%

“…Fear can be explored using a mathematical model in predator-prey interactions, which is becoming a hot topic in ecology and theoretical biology. Several studies have been carried out to see how fear affects prey population density [18,19,20]. Mondal et al [17] investigated the dynamical behavior of a predator-prey model with fear and greater food.…”

Section: Introductionmentioning

confidence: 99%

The Exponential Decay Functions for Prey and Predator Species in a Fractional-Order Ecosystem Model with Considering Global Warming Phenomena

Agarwal

Thirthar

Alaoui

2022

Preprint

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This study examines the memory eﬀect on predator-prey interactions in the face of global warming, employing a fear function with a Holling type II function to characterize the consumer prey and predator species. The eﬀect of global warming on both prey and predators was studied using the exponential decay function. The system’s equilibria are determined, and the system’s stability is established around the equilibrium points. A series of numerical simulations are done to evaluate the theoretical component of the work and show the impacts of global warming, anxiety, and fractional order on our model’s behavior.

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Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator

Cited by 39 publications

References 33 publications

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

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

A Fractional-Order Predator-Prey Model with Age Structure on Predator and Nonlinear Harvesting on Prey

The Exponential Decay Functions for Prey and Predator Species in a Fractional-Order Ecosystem Model with Considering Global Warming Phenomena

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