Global stability and bifurcation analysis in a discrete-time two prey-one predator model with help

ABSTRACT

This article examines a discrete-time predator-prey model where prey teams cooperate. Positivity and boundedness of the model solution are investigated. Positive fixed points are examined. Using an iteration scheme and the comparison principle of difference equations, we determined the sufficient condition for global stability of the positive fixed point. It is shown that the sufficient criterion for Neimark-Sacker bifurcation and flip bifurcation can be established. It is observed that the system behaves in a chaotic manner when a specific set of system parameters is selected, which are controlled by a hybrid control method. Examples are provided to illustrate our conclusions.

KEYWORDS:

• Predator-prey model
• stability
• bifurcation
• chaos control

Acknowledgments

The author would like to thank the reviewers for their helpful comments and suggestions for improving the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Debasis Mukherjee

Debasis Mukherjee is working as an Associate Professor of Mathematics, Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata, West Bengal, India. He has completed PhD degree in Mathematical Ecology from Jadavpur University, West Bengal, India, in 1992. He teaches different topics of mathematics like abstract algebra, analysis, logic, differential geometry, biomathematics, etc. He has published 96 papers on ecological and epidemiological modelling in various international journals.