Spatiotemporal dynamics of toxin producing phytoplankton–zooplankton interactions with Holling Type II functional responses

In this paper, we have studied the spatiotemporal dynamics of phytoplankton-zooplankton interactions using toxin-producing phytoplankton (TPP) with Holling type II functional responses. Toxin-producing phytoplankton (TPP) diffuses and reduces the grazing pressure on zooplankton. The grazing pressure of zooplankton is lessened by toxin-producing phytoplankton (TPP). The temporal system identifies all equilibrium points. Boundedness and local stability are established under specific parametric conditions. The conditions for the existence of a Hopf-bifurcation at the positive equilibrium by taking the half-saturation constant ($b_1$), are also discussed. In a spatial system, we explored Turing instability conditions and patterns with an emphasis on the effect of diffusion variation. Furthermore, we obtained the time evaluation pattern formation of the spatial system. Moreover, the communities of toxin-producing phytoplankton (TPP) are essential to the marine ecosystem because they lessen the mortality of zooplankton caused by grazing pressure. Finally, the basic outcomes are mentioned along with numerical results to provide some support to the analytical findings.