A chaos study of fractal–fractional predator–prey model of mathematical ecology

Ajay Kumar, Sunil Kumar, Shaher Momani and Samir Hadid

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 857-888

Abstract: This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on fractal–fractional Atangana–Baleanu (AB) and Caputo operators, we present a newly developed system of differential equations for the predator–prey system. Our study utilized the fixed point postulate to investigate the uniqueness and existence of solutions. Additionally, Ulam’s type of stability of the proposed model is established with the help of nonlinear functional analysis. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyze its behavior. The generalized non-linear system with fractal–fractional Atangana–Baleanu (AB) and Caputo non-integer operators have been solved numerically via the Toufik–Atangana (TA) scheme respectively. We have demonstrated the applicability and effectiveness of these methods by analyzing numerical simulations for the fractal–fractional predator–prey ecological model and the numerical simulation has been calculated by MATLAB programming.

Keywords: Predator–prey model; Fractal–fractional derivative; Caputo operator; Atangana–Baleanu (AB) operator; Existence and uniqueness; Toufik–Atangana (TA) technique; Lagrange polynomial; Ulam–Hyres stability; Bifurcation (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037847542300410X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:857-888

DOI: 10.1016/j.matcom.2023.09.010

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().