Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System. (13th February 2023)

• Record Type: Journal Article
• Authors: Rana, Sarker Md. Sohel
• Other Names: Matouk A. E. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2023(2023)
• Publication Date: 2023-02-13
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2023/4555469
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : In this study, we examine a discrete predator-prey system from the following two perspectives: (i) the functional response is of the Ivlev type and (ii) the prey growth rate is of the Gompertz type. We define the stability requirement for feasible fixed points. We demonstrate algebraically that if the bifurcation (control) parameter rises over its threshold value, the system encounters flip and Neimark–Sacker (NS) bifurcations in the vicinity of the interior fixed point. We explicitly establish the existence requirements and direction of bifurcations via the center manifold theory. Analytical findings are validated by numerical simulations, which are used to highlight the occurrence of instability and chaotic dynamics in the system. In order to regulate the chaotic trajectories that exist in the system, we adopt a feedback control approach.