Subcritical Neimark–Sacker bifurcation and hybrid control in a discrete-time Phytoplankton–Zooplankton model

Abstract

In this paper, we explore the local dynamical behavior with different topological classifications around fixed points, Neimark–Sacker bifurcation and hybrid control in the discrete-time Phytoplankton–Zooplankton model. More precisely, we have investigated the local dynamical behavior with different topological classifications around trivial, semitrivial and interior fixed points of the two-dimensional Phytoplankton–Zooplankton model, respectively. The existence of possible bifurcations around fixed points is also investigated, and it is proved that there exists no flip bifurcation around trivial and semitrivial fixed points but around interior fixed point, the model undergoes Neimark–Sacker bifurcation only. Moreover, hybrid control strategy is utilized for controlling Neimark–Sacker bifurcation in the Phytoplankton–Zooplankton model. Lastly, theoretical results are verified numerically.