Dynamical Analysis in a Discrete Fractional Order Harvested Predator-Prey Model Incorporating Fear Effect and Refuge

Abstract

This paper examines the dynamics of a discrete fractional-order predator-prey model, incorporating the effects of fear, prey refuge, and population harvesting. The fractional-order framework, which accounts for memory-dependent processes, provides a more accurate depiction of biological interactions than traditional integer-order models. Fear is modeled as a factor that reduces predator-prey encounters, while prey refuge offers a sanctuary, altering population dynamics. The inclusion of harvesting further complicates prey population regulation. We identify the system’s equilibrium points and conduct a local stability analysis, focusing on the conditions that lead to stability, instability, and bifurcation. Specifically, we examine the Neimark-Sacker bifurcation, where a stable fixed point evolves into a closed periodic orbit. Numerical simulations corroborate the analytical findings, illustrating the pivotal roles that fear, refuge, and harvesting play in shaping system stability and long-term behavior.