HOPF BIFURCATION AND GLOBAL STABILITY OF A PREDATOR–PREY MODEL WITH ALTERNATIVE RESOURCE AND CANNIBALISM-Reference-Cited by-同舟云学术

HOPF BIFURCATION AND GLOBAL STABILITY OF A PREDATOR–PREY MODEL WITH ALTERNATIVE RESOURCE AND CANNIBALISM

Published:2023-01 Issue:10 Volume:31 Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

LIU JUAN¹,UPADHYAY RANJIT KUMAR²,AGRAWAL RASHMI³,ZEB ANWAR⁴^ORCID,SAEED TAREQ⁵^ORCID,AHMAD ZAHID⁴

Affiliation:

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

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

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

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

5. 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

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.

Funder

Institutional Fund Projects

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X23400844

Reference31 articles.

1. Hopf bifurcation in a delayed Lokta–Volterra predator–prey system

2. Qualitative analysis of a Lotka–Volterra predator–prey system with migration

3. Local stability analysis on Lotka‐Volterra predator‐prey models with prey refuge and harvesting

4. On the existence of almost periodic solutions of impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms

5. Dynamical analysis on a predator–prey model with stage structure and mutual interference

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1. EDITORIAL SPECIAL ISSUE: PART IV-III-II-I SERIES;Fractals;2023-01