Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting

Debasis Mukherjee

doi:10.33434/cams.1171482

EN

Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting

Abstract

This article studies a discrete-time Leslie-Gower two predator-one prey system with Michaelis-Menten type prey harvesting. Positivity and boundedness of the model solution are investigated. Existence and stability of fixed points are examined. Using an iteration scheme and the comparison principle of difference equations, we find out the sufficient condition for global stability of the positive fixed point. It is shown that the sufficient criterion for Neimark-Sacker bifurcation can be developed. It is observed that the system behaves in a chaotic manner when a specific set of system parameters is chosen, which are regulated by a hybrid control method. Examples are provided to illustrate our conclusions.

Keywords

Predator-prey model , Leslie-Gower , Michaelis-Menten type prey harvesting , stability , bifurcation , chaos control

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Debasis Mukherjee ^*
India

Publication Date

March 31, 2023

Submission Date

September 6, 2022

Acceptance Date

March 29, 2023

Published in Issue

Year 2023 Volume: 6 Number: 1

DOI

https://doi.org/10.33434/cams.1171482

IZ

https://izlik.org/JA62RS34CB

APA

Mukherjee, D. (2023). Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting. Communications in Advanced Mathematical Sciences, 6(1), 1-18. https://doi.org/10.33434/cams.1171482

AMA

1.Mukherjee D. Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting. Communications in Advanced Mathematical Sciences. 2023;6(1):1-18. doi:10.33434/cams.1171482

Chicago

Mukherjee, Debasis. 2023. “Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model With Michaelis-Menten Type Prey Harvesting”. Communications in Advanced Mathematical Sciences 6 (1): 1-18. https://doi.org/10.33434/cams.1171482.

EndNote

Mukherjee D (March 1, 2023) Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting. Communications in Advanced Mathematical Sciences 6 1 1–18.

IEEE

[1]D. Mukherjee, “Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting”, Communications in Advanced Mathematical Sciences, vol. 6, no. 1, pp. 1–18, Mar. 2023, doi: 10.33434/cams.1171482.

ISNAD

Mukherjee, Debasis. “Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model With Michaelis-Menten Type Prey Harvesting”. Communications in Advanced Mathematical Sciences 6/1 (March 1, 2023): 1-18. https://doi.org/10.33434/cams.1171482.

JAMA

1.Mukherjee D. Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting. Communications in Advanced Mathematical Sciences. 2023;6:1–18.

MLA

Mukherjee, Debasis. “Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model With Michaelis-Menten Type Prey Harvesting”. Communications in Advanced Mathematical Sciences, vol. 6, no. 1, Mar. 2023, pp. 1-18, doi:10.33434/cams.1171482.

Vancouver

1.Debasis Mukherjee. Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting. Communications in Advanced Mathematical Sciences. 2023 Mar. 1;6(1):1-18. doi:10.33434/cams.1171482