ArticleOpen Access

DYNAMICS OF A PREY–PREDATOR MODEL INCORPORATING GESTATION TIME DELAY AND FEAR EFFECT

School of Science, Bengbu University, Bengbu 233030, P. R. China

Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, Jharkhand, India

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RASHMI AGRAWAL

Department of Humanities and Science, Indian Institute of Information Technology Dharwad, Karnataka 580009, India

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ANWAR ZEB

https://orcid.org/0000-0002-5460-3718

Department of Mathematics, COMSATS University, Islamabad, Abbottabad, Pakistan

E-mail Address: anwar@cuiatd.edu.pk

Corresponding author.

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, and

TAREQ SAEED

https://orcid.org/0000-0002-0170-5286

Financial Mathematics and Actuarial Science, (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

E-mail Address: tsalmalki@kau.edu.sa

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https://doi.org/10.1142/S0218348X23401552Cited by:4 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems IV
Guest Editors: Yeliz Karaca, Dumitru Baleanu, Majaz Moonis, Yu-Dong Zhang and Osvaldo Gervasi

Abstract

The anti-predator element because of fear from predator population in prey–predator models has an excellent significance and it is able to lessen the duplicate of prey population to a positive degree. In this paper, a delayed prey–predator model including fear effect and predator-taxis sensitivity is studied. Local stability and occurrence of Hopf bifurcation are analyzed by fixing the time delay as the bifurcating parameter. Then, a series of sufficient criteria for global stability is established by designing a suitable Lyapunov function. Furthermore, direction and stability of the Hopf bifurcation are studied. Lastly, numerical simulation outcomes are performed to confirm our theoretical findings.

Keywords:

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Vol. 31, No. 10

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History

Received 8 April 2022

Accepted 11 February 2023

Published: October 7, 2023

Information

This is an Open Access article in the “Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems: Part IV”, edited by Yeliz Karaca https://orcid.org/0000-0001-8725-6719 (University of Massachusetts Chan Medical School, USA), Dumitru Baleanu https://orcid.org/0000-0002-0286-7244 (Cankaya University, Turkey & Institute of Space Sciences, Romania), Majaz Moonis https://orcid.org/0000-0002-9747-0003 (University of Massachusetts Chan Medical School, USA), Yu-Dong Zhang https://orcid.org/0000-0002-4870-1493 (University of Leicester, Leicester, UK) & Osvaldo Gervasi https://orcid.org/0000-0003-4327-520X (Perugia University, Perugia, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 (CC BY-NC-ND) License which permits use, distribution and reproduction, provided that the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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DYNAMICS OF A PREY–PREDATOR MODEL INCORPORATING GESTATION TIME DELAY AND FEAR EFFECT

Abstract

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