Seminar

"Fractional-Order Predator–Prey Models with Nonlinear Functional Responses"

Chaimaa Assila

Laboratory of Mathematics, Computer Science and Applica-

tions, Information Security(LABMIA-SI)

Mohammed V University, Morocco

November 5, 2025, 13:00

In this presentation, we focus on the mathematical modeling and analysis of predator–prey systems using ordinary, fractional, and delayed differential equations. The main goal is to understand how memory effects, time delays, and environmental factors, such as temperature changes, influence ecological dynamics. The first part examines a delayed predator–prey system, highlighting how time

delays can induce Hopf bifurcations and comparing integer-order and fractional-order formulations. The second part incorporates the Crowley–Martin functional response, together with fear and climate effects, to study how predation pressure and environmental changes jointly shape species interactions. Numerical simulations reveal complex dynamical behaviors, including oscillations

and stability changes. The results demonstrate the advantages of fractional-order modeling in capturing ecological memory and subtle nonlinear interactions, providing new insights into predator–prey dynamics under realistic environmental conditions.