Complex dynamics analysis of a non-smooth predator-prey model with stage structure and threshold-dependent refuge mechanism
摘要
This paper proposes a novel three-dimensional Filippov predator-prey model to investigate the integrated effects of predator behavioral switching, stage structure, and threshold-induced non-smooth control mechanisms on system stability and dynamical behavior. Through qualitative analysis, we investigate the stability of equilibria and establish the existence of periodic solutions. Our study reveals that while the system can stabilize within the sliding region to achieve population regulation, rich bifurcation phenomena occur in this regime. Specifically, when a key parameter exceeds the critical threshold, the system undergoes a boundary equilibrium bifurcation and a global sliding bifurcation: the former destabilizes the stable positive equilibrium and leads to its replacement by a stable pseudo-equilibrium, while the latter induces the collapse of the limit cycle, signifying a transition from periodic oscillations to a stable equilibrium. Numerical simulations reveal rich ecological dynamics, including overcompensation, periodic oscillations, and threshold-induced state transitions. These findings highlight the crucial role of refuge mechanisms in regulating ecological stability and provide theoretical support for population management and sustainable utilization strategies.