Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge. (February 2021)

• Record Type: Journal Article
• Authors: Kaur, Rajinder Pal; Sharma, Amit; Sharma, Anuj Kumar
• Is Part Of: Chaos, solitons and fractals. Volume 143(2021)
• Publication Date: 2021-02
• Subjects: Plankton -- Refuge -- Fear -- Hopf-bifurcation -- Centre manifold theorem; 34C11 -- 34C23 -- 34D20 -- 92B05 -- 92D40; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110563
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: In this paper, we analyze the impact of anti-predator behavior due to fear effect and zooplankton refuge on a 3-D plankton-fish dynamical system involving phytoplankton, zooplankton, and fish species. We have explored the plankton dynamics through the defence mechanism adopted by zooplankton due to the fear of top predator (fish) in the marine ecosystem. Ecologically, we have shown that the fear effect and zooplankton refuge has the following impacts on the dynamics of the model system: (1) The zooplankton refuge increases their biomass gradually and induces extinction of its predator (fish). (2) The fear of top predator has a little bit impact on the population densities of prey, but it affects the density of top predator fish. It is determined that zooplankton refuge induces some mechanism for controlling the planktonic blooms in the presence of a high fear effect. It is also observed that the low level of fear effect K can terminate planktonic blooms in the presence of high zooplankton refuge. The present ecological model exhibits various intervals of zooplankton refuge and fear effect for maintaining the sustainability and co-existence of the plankton-fish ecosystem. Abstract: In this paper, we analyze the impact of anti-predator behavior due to fear effect ( K ) and zooplankton refuge ( r 1 ) 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 r 1 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 r 1 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.