Global stability of the interior equilibrium and the stability of Hopf bifurcating limit cycle in a model for crop pest control

Aeshah A. Raezah; Jahangir Chowdhury; Fahad Al Basir; Aeshah A. Raezah; Jahangir Chowdhury; Fahad Al Basir

doi:10.3934/math.20241179

AIMS Mathematics

2024, Volume 9, Issue 9: 24229-24246. doi: 10.3934/math.20241179

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Global stability of the interior equilibrium and the stability of Hopf bifurcating limit cycle in a model for crop pest control

1.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia
2.
Department of Applied Science, RCC Institute of Information Technology, Kolkata, India
3.
Department of Mathematics, Asansol Girls' College, Asansol-4, West Bengal, India

Received: 23 June 2024 Revised: 31 July 2024 Accepted: 09 August 2024 Published: 16 August 2024

Mathematical modeling and analysis of a crop-pest interacting system helps us to understand the dynamical properties of the system such as stability, bifurcations and chaos. In this article, a predator-prey type mathematical model for pest control using bio-pesticides has been analysed to study the global stability property of the interior equilibrium point. Moreover, the occurrence and orbital stability of Hopf bifurcating limit cycle solutions have been studied using ref30's conditions. Analytical and numerical results show that the interior equilibrium of the pest control model is globally asymptotically stable. Also, Hopf bifurcating occurs when the bifurcation parameter crosses the critical value, and the bifurcating periodic solution is found to be stable.
- mathematical model,
- Lyapunov function,
- global stability,
- Hopf bifurcation,
- stability of limit cycle,
- ref30's condition
Citation: Aeshah A. Raezah, Jahangir Chowdhury, Fahad Al Basir. Global stability of the interior equilibrium and the stability of Hopf bifurcating limit cycle in a model for crop pest control[J]. AIMS Mathematics, 2024, 9(9): 24229-24246. doi: 10.3934/math.20241179

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Abstract

Mathematical modeling and analysis of a crop-pest interacting system helps us to understand the dynamical properties of the system such as stability, bifurcations and chaos. In this article, a predator-prey type mathematical model for pest control using bio-pesticides has been analysed to study the global stability property of the interior equilibrium point. Moreover, the occurrence and orbital stability of Hopf bifurcating limit cycle solutions have been studied using ref30's conditions. Analytical and numerical results show that the interior equilibrium of the pest control model is globally asymptotically stable. Also, Hopf bifurcating occurs when the bifurcation parameter crosses the critical value, and the bifurcating periodic solution is found to be stable.

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