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

被引：0

作者：

Liu, Juan ^{[1
]}

Upadhyay, Ranjit kumar ^{[2
]}

Agrawal, Rashmi ^{[3
]}

Zeb, Anwar ^{[4
]}

Saeed, Tareq ^{[5
]}

Ahmad, Zahid ^{[4
]}

机构：

[1] Bengbu Univ, Sch Sci, Bengbu 233030, Anhui, Peoples R China

[2] Indian Inst Technol, Indian Sch Mines, Dept Math & Comp, Dhanbad 826004, Jharkhand, India

[3] Indian Inst Informat Technol Dharwad, Dept Humanities & Sci, Dharwad 580009, Karnataka, India

[4] COMSATS Univ Islamabad, Dept Math, Abbottabad, Pakistan

[5] King Abdulaziz Univ, Fac Sci, Dept Math, Financial Math & Actuarial Sci FMAS Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2023年 / 31卷 / 10期

关键词：

Delay; Hopf Bifurcation; Periodic Solutions; Predator-prey Model with Cannibalism; Stability; STAGE STRUCTURE; DYNAMICS; SYSTEM; DISCRETE; DISEASE; FEAR;

D O I：

10.1142/S0218348X23400844

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：14

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