Predation fear and its carry-over effect in a fractional order prey–predator model with prey refuge

Abstract

This research article centers on the formulation and analysis of a novel prey–predator model that integrates the impacts of predation fear, prey refuge, and carry-over effects. The model is formulated and analyzed using fractional differential equations (FDEs). The model incorporates ecological concepts such as anti-predator behaviours and memory effects to maintain a better understanding of prey–predator interactions. The mathematical model is developed based on a basic prey–predator model with a Michelis–Menten functional response and includes fear-induced carry-over effects, prey refuge, and fractional order derivatives. The study investigates the well-posedness, stability, and Hopf bifurcation of the proposed model and conducts detailed numerical investigations. The integration of different anti-predatory mechanisms and the use of FDEs contribute to a comprehensive understanding of the dynamics of prey–predator interactions and provide useful insights into the complexities of ecological systems.