Dynamical Complexities of a Discrete Ivlev-Type Predator-Prey System

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 t...

Full description

Saved in:
Bibliographic Details
Published inDiscrete dynamics in nature and society Vol. 2023; pp. 1 - 14
Main Author Rana, Sarker Md. Sohel
Format Journal Article
LanguageEnglish
Published New York Hindawi 13.02.2023
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Bifurcation theory
Centre manifold theory
Dynamic stability
Feedback control
Numerical analysis
Predation
Predator-prey simulation
Predators
Simulation methods
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2023/4555469