Incorporating Prey Refuge in a Prey-Predator Model with Beddington-DeAngelis Type Functional Response: A Comparative Study on Intra-Speciﬁc Competition

Molla, Hafizul; Rahman, Md. Sabiar; Sarwardi, Sahabuddin

doi:10.5890/dnc.2020.09.005

Cited by 2 publications

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“…In this study, we have considered x, y as the prey and predator species respectively and δxy as the amount of nonlinear prey refuge (cf. [17,[19][20][21]) admissible for t 0 with 0 x(1 − δy) x. The factor y y+h comes into predator growth function to decrease the predator growth rate because, if a predator eats more, it will be less likely to die from starvation or from the consequences of weakness due to hunger; and it is positive for any value of functional response, because a predator is highly unlikely to live forever.…”

Section: Model Compositionmentioning

confidence: 99%

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Predator-prey dynamics with Allee effect on predator species subject to intra-specific competition and nonlinear prey refuge

Molla¹,

Sarwardi²,

Sajid³

2021

J. Math. Computer Sci.

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A modified version of our previously analyzed prey-predator refuge model is presented in this article by introducing Allee effect on the predator species and mutual interference among the predators. Possible number of coexistence equilibrium points are investigated with the help of prey and predator nullcline. The local stability and Hopf-bifurcation conditions are established around the coexistence equilibria. We have also discussed the nature of Hopf-bifurcation around the unique coexistence equilibrium point of the system as well. Finally, a comprehensive numerical simulation is carried out to justify our obtained analytical findings.

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Section: Model Compositionmentioning

confidence: 99%

“…Biological description and dimension of the parameters used in the model (2.3) have been chosen from[19] and[21]: V stands for volume of the species and T for time.…”

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confidence: 99%