Analysis and Control of Chaotic Behaviour in a Plankton-Fish Interaction System with Fear and Refuge - Amit Sharma; Rajinder pal Kaur (Department of Mathematics, Universitas Negeri Gorontalo, 2025)
Controlling chaos in plankton-fish dynamics has been predominantly remained a rationale of many ecologists for managing and preserving ecosystem. In this paper, we have introduced a mathematical model consisting of phytoplankton, zooplankton, and fish population with a motive to study the simultaneous impact of prey refuge and fear. We have determined the existence of all feasible biological equilibria and proposed certain conditions of local stability of the given system around it. The Hopf-bifurcation analysis is carried out by considering phytoplankton refuge (n1), zooplankton refuge (n2), and fear effect (L) as significant bifurcation parameters. It is seen that fear of top predator mitigate unpredictable(chaotic) behavior of the plankton system and induce system stability for L ≥ 1.09. Our investigations reveal that the defense mechanism developed by prey species due to the fear of predator population, namely n1 and n2 can also terminate chaos from the system. It is found that the given dynamical system remains stable in the intervals n1 ∈ [0.71, 0.73] and n2 ∈ [0.73, 0.75]. We have applied feedback and non-feedback control mechanisms to stabilize the chaotic trajectories of the plankton-fish dynamics. All analytical findings are substantiated using numerical simulation.