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

Juan Liu, Ranjit Kumar Upadhyay, Rashmi Agrawal, Anwar Zeb and Tareq Saeed ()
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Juan Liu: School of Science, Bengbu University, Bengbu 233030, P. R. China
Ranjit Kumar Upadhyay: ��Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, Jharkhand, India
Rashmi Agrawal: ��Department of Humanities and Science, Indian Institute of Information Technology Dharwad, Karnataka 580009, India
Anwar Zeb: �Department of Mathematics, COMSATS University, Islamabad, Abbottabad, Pakistan
Tareq Saeed: �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

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-10

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: Fear Effect; Delay; Predator–Prey Model; Hopf Bifurcation; Global Stability; Periodic Solutions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23401552

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