ItemArticle

Stability and bifurcation analysis of a fractional-order preypredator model with ratio-dependent functional response

Title
Stability and bifurcation analysis of a fractional-order preypredator model with ratio-dependent functional response
Creator
Alraddadi, Ibrahim; Perumal, Ramesh; Ahmed, Rizwan; Khan, Jawad; Lee, Youngmoon
Description
This paper explores the dynamics of a fractional preypredator system with a ratio-dependent functional response with memory and hereditary effects in predatorprey interactions. The model is developed by the Caputo fractional derivative, and the existence, uniqueness, positivity, and boundedness of solutions are proven to satisfy biological reality. Stability conditions for local and global stability of both predator-free and coexistence equilibria are proven through linearization and Lyapunov function techniques. The fractional order is used as a bifurcation parameter, and the appearance of Hopf bifurcations is analytically explained with demonstration of the influence of memory on oscillations. To examine discrete-time dynamics, the piecewise constant argument is used to derive a discrete counterpart of the fractional model. The discrete model indicates a wide range of rich complex oscillatory phenomena, including period-doubling and NeimarkSacker bifurcations, leading to periodic, quasiperiodic, and chaotic oscillations. Numerical computations, including bifurcation diagrams, phase portraits, and Lyapunov exponents, verify the analytical results and describe the routes of transition to chaos. A comparative analysis to compare integer- and fractional-order cases indicates that memory effects enhance dynamical richness and sensitivity to parameters. The study provides a unified framework relating continuous fractional dynamics and their discrete implementations and provides additional insight into how memory and discretization interact to modify stability and bifurcation in ecological models. 2026 the Author(s),
Source
AIMS Mathematics;Volume;11;Issue;1;pp.1412-1448
Date
01-01-2026
Publisher
American Institute of Mathematical Sciences
Subject
bifurcation; chaos; fractional-order; preypredator model; stability
Coverage
Alraddadi I., Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia; Perumal R., Department of Mathematics, Madanapalle Institute of Technology & Science (MITS), Deemed to be University, Madanapalle,, Andhra, Pradesh, India; Ahmed R., Department of Mathematics, Air University Multan Campus, Multan, 60001, Pakistan; Khan J., School of Computing, Gachon University, Seongnam, 13120, South Korea; Lee Y., Department of Robotics, Hanyang University, Ansan, 15588, South Korea, Department of Applied AI, Hanyang University, Ansan, 15588, South Korea
Rights
All Open Access; Gold Open Access
Relation
ISSN: 24736988;
Format
online
Language
English
Type
Article

Citation

Alraddadi, Ibrahim; Perumal, Ramesh; Ahmed, Rizwan; Khan, Jawad; Lee, Youngmoon, “Stability and bifurcation analysis of a fractional-order preypredator model with ratio-dependent functional response,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 19, 2026, https://archives.christuniversity.in/items/show/23595.

Output Formats