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Fractal Fract
Volume 9
Issue 1
10.3390/fractalfract9010045
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Article

Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect

by
Vinoth Seralan
1,
Rajarathinam Vadivel
2,
Nallappan Gunasekaran
3 and
Taha Radwan
4,*
1
Center for Nonlinear and Complex Networks, SRM Institute of Science and Technology, Ramapuram, Chennai 600089, Tamilnadu, India
2
Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand
3
Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, China
4
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
*
Author to whom correspondence should be addressed.
Fractal Fract. 2025, 9(1), 45; https://doi.org/10.3390/fractalfract9010045
Submission received: 16 December 2024 / Revised: 7 January 2025 / Accepted: 13 January 2025 / Published: 16 January 2025
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Abstract

This study examines a Caputo-type fractional-order food chain model, considering the Holling type II functional response with the vigilance effect. The model explores the interaction dynamics of the food chain model, which consists of prey, middle predators, and top predators. Additionally, habitat complexity is integrated into the model, which is assumed to reduce predation rates by lowering the encounter rates between predators and prey. All possible feasible equilibrium points are determined and the stability of our proposed model is explored near the equilibrium points. To support the analytical findings, numerical simulation results are given in terms of time series, phase portraits, and bifurcation diagrams. It is discovered that the proposed model can become more stable under a fractional-order derivative. Moreover, the interplay between the vigilance effect and habitat complexity is shown to influence the existence of stable and periodic dynamics.
Keywords: food chain; habitat complexity; stability; fractional derivatives; vigilance food chain; habitat complexity; stability; fractional derivatives; vigilance

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MDPI and ACS Style

Seralan, V.; Vadivel, R.; Gunasekaran, N.; Radwan, T. Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect. Fractal Fract. 2025, 9, 45. https://doi.org/10.3390/fractalfract9010045

AMA Style

Seralan V, Vadivel R, Gunasekaran N, Radwan T. Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect. Fractal and Fractional. 2025; 9(1):45. https://doi.org/10.3390/fractalfract9010045

Chicago/Turabian Style

Seralan, Vinoth, Rajarathinam Vadivel, Nallappan Gunasekaran, and Taha Radwan. 2025. "Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect" Fractal and Fractional 9, no. 1: 45. https://doi.org/10.3390/fractalfract9010045

APA Style

Seralan, V., Vadivel, R., Gunasekaran, N., & Radwan, T. (2025). Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect. Fractal and Fractional, 9(1), 45. https://doi.org/10.3390/fractalfract9010045

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