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Dynamics Of A Prey–Predator Model Incorporating Gestation Time Delay And Fear Effect

Author

Listed:
  • 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)

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.

Suggested Citation

  • Juan Liu & Ranjit Kumar Upadhyay & Rashmi Agrawal & Anwar Zeb & Tareq Saeed, 2023. "Dynamics Of A Prey–Predator Model Incorporating Gestation Time Delay And Fear Effect," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x23401552
    DOI: 10.1142/S0218348X23401552
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