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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Dynamics of the Leslie Type Predator-Prey Model with Effect of Fear and Delay in the Prey Population

Discontinuity, Nonlinearity, and Complexity 12(2) (2023) 365--380 | DOI:10.5890/DNC.2023.06.010

$^{1} $ Department of Mathematics, Dr. R. V. Arts and Science College, Coimbatore, Tamilnadu, India

$^{2}$ Department of Mathematics, M. Kumarasamy College of Engineering, Karur, Tamilnadu, India

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Abstract

We present the dynamics of the predator-prey model of Leslie type by introducing fear and gestation delay in the prey population to get a more realistic model. It is assumed that the predator consumes prey in the form of Beddington DeAngelis functional response. For all positive equilibrium points, the existence and local stability analysis is discussed. The condition for the local stability of coexisting equilibrium point for both delayed and non-delayed model is provided by using the Routh-Hurwitz criterion. The global stability property of the coexisting equilibrium point is analyzed with the help of constructing a suitable Lyapunov function. Also, the model shows bifurcation behavior, particularly Hopf-bifurcation at coexisting equilibrium point for both delayed and non-delayed model are proven analytically. Also, the analytical results are verified numerically in each section.

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