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

Author:

Raezah Aeshah A.1,Chowdhury Jahangir2,Al Basir Fahad3

Affiliation:

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

Abstract

<p>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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference29 articles.

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2. W. J. Lewis, J. C. Van Lenteren, S. C. Phatak, J. H. Tumlinson, A total system approach to sustainable pest management, Proc. Natl. Acad. Sci., 94, (1997), 12243–12248. https://doi.org/10.1073/pnas.94.23.1224

3. M. L. Flint, R. Van den Bosch, Introduction to integrated pest management, Springer Science & Business Media, (2012).

4. E. Beltrami, Mathematics for dynamic modeling, Academic press, (2014).

5. R. M. May, Stability and complexity in model ecosystems, Princeton university press, (2019).

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