Dynamics of a Food Chain Model Using the Caputo Fractional Derivative (Journal of Mathematical Modeling and Fractional Calculus, 2025)
This work investigates a fractional-order food chain model based on the Caputo operator, taking into account resource availability, competition, and predation. The dynamics of the food chain are bet ter represented using fractional calculus, which takes into account long-range interactions and previous dependency. Analytical and numerical simulations reveal information about the resilience, persistence, and stability of biological communities under fractional order dynamics. The model includes a three species food chain, as well as environmental contamination. We begin by confirming the model’s uniqueness, nonnegativity, and boundedness. We also examine numerous conditions for the presence of equilibrium and local stability. Second, a controller is proposed, and the global stability of the positive equilibrium point is investigated using the Lyapunov method. The proposed model solution was estimated using the fractional iterative technique, and numerical simulations were carried out to validate the theoretical results.
Keywords: Food chain model; Caputo fractional operator; Positivity and boundedness; Local stability; Chaos and error analysis