Global analysis on a nonlinear diffusion system with fear effect, protection zone and Ivlev functional response

Abstract

This paper investigates a novel nonlinear diffusive Ivlev-type predator-prey system that synergistically integrates fear effect and protection zone. By analyzing bifurcation structure of positive steady-states emanating from semi-trivial steady-states, and employing Leray-Schauder degree theory, we characterize how these combined factors dictate the multiplicity, uniqueness and stability of positive steady-states. Additionally, we examine the asymptotic behaviors of positive steady-states induced by the predator growth rate and prey diffusion rate. The long-term dynamical behaviors of the system are finally revealed. The findings reveal that the interplay of fear effect, protection zone and Ivlev-type interaction term generates unprecedented dynamical regimes in traditional models with fewer ecological factors, and offers both theoretical insights into complex ecosystems and practical guidance for conservation strategies. Biologically speaking, such joint effects help to showcase their synergistic roles in shaping population dynamics and ecological stability.