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Hopf Bifurcation And Global Stability Of A Predator–Prey Model With Alternative Resource And Cannibalism

Author

Listed:
  • JUAN LIU

    (School of Science, Bengbu University, Bengbu, Anhui 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, Dharwad 580009, Karnataka, 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)

  • ZAHID AHMAD

    (�Department of Mathematics, COMSATS University Islamabad, Abbottabad, Pakistan)

Abstract

In this study, we present a delayed predator–prey model with cannibalism including a prey, a juvenile predator and an adult predator. The adult predator hunts not only the prey but also the juvenile predator. The alternative resource is considered to reduce cannibalism in predator species. The main results are demonstrated by local stability and Hopf bifurcation. Sufficient criteria for local stability of the interior equilibrium point and the exhibition of a Hopf bifurcation are derived. Global stability is analyzed via designing a suitable Lyapunov function. Additionally, stability of the Hopf bifurcation is explored. Finally, numerical simulations are executed to validate the obtained results.

Suggested Citation

  • Juan Liu & Ranjit Kumar Upadhyay & Rashmi Agrawal & Anwar Zeb & Tareq Saeed & Zahid Ahmad, 2023. "Hopf Bifurcation And Global Stability Of A Predator–Prey Model With Alternative Resource And Cannibalism," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-14.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x23400844
    DOI: 10.1142/S0218348X23400844
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