Analysis and Control of Chaotic Behaviour in a Plankton-Fish Interaction System with Fear and Refuge

Amit Sharma, Rajinder pal Kaur

Abstract


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.


Keywords


Plankton; Fear; Refuge; Hopf-bifurcation; Chaos

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DOI: https://doi.org/10.37905/jjbm.v6i4.33743

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