Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge

Abstract

In this paper, we analyze the impact of anti-predator behavior due to fear effect (K) and zooplankton refuge (r1) on a 3-D plankton-fish dynamical system involving phytoplankton, zooplankton, and fish species. We assume that zooplankton species have developed defense mechanisms against fish predation. The fear of fish predation altered anti-predator defenses, which affects the growth of the fish population. On the other hand, zooplankton refuge reduces fish induced mortality of zooplankton and plays a significant role in controlling phytoplankton growth. The density of fish species is suppressed in the presence of high refuge and the anti-predator response of zooplankton. It is determined that K and r1 can influence not only plankton-fish demography but also induce some mechanism to terminate planktonic blooms. Our mathematical study reveals that the low level of fear can stabilize the system dynamics in the presence of high rate of zooplankton refuge. Moreover, the low rate of zooplankton refuge can exclude complexity from the plankton-fish ecosystem in the presence of strong anti-predator responses of zooplankton. We have established the existence of all feasible biological equilibria and derived the conditional local and global stability of the given system around it. The Hopf-bifurcation analysis is carried out by considering K and r1 as bifurcation parameters. The direction of bifurcating solutions is also determined using the centre manifold arguments. Numerical simulation is carried out to substantiate our analytical findings.