Stability, bifurcation, and chaos control in a discrete predator-prey model with strong Allee effect

AIMS Mathematics

article

Ali Al Khabyah¹  Rizwan Ahmed²  Muhammad Saeed Akram³  Shehraz Akhtar⁴ 

[1] Department of Mathematics, College of Science, Jazan University, New Campus;Department of Mathematics, Air University Multan Campus;Department of Mathematics, Faculty of Science, Ghazi University;Department of Mathematics, The Islamia University of Bahawalpur Rahim Yar Khan Campus

关键词: predator-prey;    Holling type-Ⅱ;    Allee effect;    stability;    bifurcation;   

DOI  :  10.3934/math.2023408

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

This work considers a discrete-time predator-prey system with a strong Allee effect. The existence and topological classification of the system's possible fixed points are investigated. Furthermore, the existence and direction of period-doubling and Neimark-Sacker bifurcations are explored at the interior fixed point using bifurcation theory and the center manifold theorem. A hybrid control method is used for controlling chaos and bifurcations. Some numerical examples are presented to verify our theoretical findings. Numerical simulations reveal that the discrete model has complex dynamics. Moreover, it is shown that the system with the Allee effect requires a much longer time to reach its interior fixed point.

【 授权许可】

CC BY