Influence of nanoparticles on the spatiotemporal dynamics of phytoplankton-zooplankton interaction system

In this work, we study the Nanoparticles (NPs) impact on a phytoplankton-zooplankton interaction model with Ivlev-like and Holling type-II functional responses. We found that the growth rate of phytoplankton reduces due to NPs. In the non-spatial model, we investigated boundedness, stability, bifurcation and chaos. The stability criteria is determined using the Routh-Hurwitz criterion. Hopf bifurcation is demonstrated with parameter K, which represents the NPs carrying capacity while interacting with phytoplankton. The normal theory is used to examine the Hopf bifurcation direction and the stability of bifurcating periodic solutions. Moreover, the stability of non-hyperbolic equilibrium points have been determined using the Center Manifold theorem. Also, the parameter beta, which represents the interaction rate between NPs and phytoplankton, exhibits chaotic behavior. Furthermore, we also investigated Hopf bifurcation and Turing instability in spatial model systems. This study demonstrates that NPs can influence the dynamics of the system in a balanced environment.