Non-smooth dynamics emerging from predator-driven discontinuous prey dispersal

In ecology, the refuge protection of prey plays a significant role in dynamics interactions between and predator. this paper, we investigate non-smooth prey–predator mathematical model characterized by density-dependent intermittent prey. The assumes population density predator as an index for to decide on when avail or discontinue protection, representing level apprehension predators. We apply Filippov’s regularization approach study obtain sliding segment system. criterion existence regular virtual equilibria, boundary equilibrium, tangent points, pseudo-equilibria Filippov conditions visibility (or invisibility) points are derived. equilibrium bifurcation, boundary-node bifurcation pseudo-saddle-node bifurcation. Further, examine effects dispersal delay system associated with vigilance identifying density. observe that hysteresis produces stable limit cycles around threshold some bounded region phase plane. Moreover, find play their refuge-dispersion dynamics.