Spatiotemporal Dynamic of Toxin Producing Phytoplankton (TPP)-Zooplankton Interaction

Abstract.The present paper deals with a toxin producing phytoplankton (TPP)-zooplankton interaction in spatial environment in the context of phytoplankton bloom. In the absence of diffusion the stability of the given system in terms of co-existence and hopf bifurcation has been discussed. After that TPP-zooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both population. It has been obtained that in the pres- ence of diffusion given system becomes unstable (Turing instability) under certain conditions. Moreover, by applying the normal form theory and the center manifold reduction for par- tial differential equations (PDEs), the explicit algorithm determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions is derived. Finally, numerical simulations supporting the theoretical analysis are also included.