Bifurcation dynamics of a harvested predator-prey model

Authors

• Hala H. Emam, Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, EgyptFollow
• Mohamed F. Abouelenein, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi ArabiaFollow
• Mona Anis, Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, EgyptFollow
• M. Y. Hamada, Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, EgyptFollow
• F. A. Atia, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi ArabiaFollow
• H. El-Metwally, Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, EgyptFollow

Abstract

In ecosystems, the harvesting effect is essential to preserving the relationships between prey and predator. This work examines a model of predator-prey in discrete time with harvesting. The Jacobian matrix's eigenvalues are calculated for the associated fixed points. We examine the dynamical and qualitative analysis of this model, look into the criteria for stability and bifurcation, and analyze analytical results that show the rich dynamics and complexity of this model. We give sufficient circumstances for the Period-doubling at the interior equilibrium point by employing the harvesting effect. The discrete system's chaos control is carried out, and the outcomes are supported by numerical simulations. Prey-predator interactions have been found to be significantly impacted by the harvesting effect.

Recommended Citation

Emam, Hala H.; Abouelenein, Mohamed F.; Anis, Mona; Hamada, M. Y.; Atia, F. A.; and El-Metwally, H. (2026) "Bifurcation dynamics of a harvested predator-prey model," Mathematical Modelling and Numerical Simulation with Applications: Vol. 6: Iss. 3, Article 8.
DOI: https://doi.org/10.53391/2791-8564.1040
Available at: https://mmnsa.researchcommons.org/journal/vol6/iss3/8