The dynamics of viral infection in toxin producing phytoplankton and zooplankton system with time delay

Abstract

Dynamical behaviour of virally infected toxin producing phytoplankton and zooplankton system is explored with the assumption that toxin liberation is not an instantaneous process. It is further hypothesized that the infected phytoplankton species do recover from disease. It is established that time delay in toxin liberation process can destabilize the otherwise stable equilibrium state. The coexistence of all the species is observed through the periodic oscillations as a result of Hopf bifurcation. Normal form theory and central manifold arguments are applied to determine the direction of Hopf bifurcation and stability of bifurcating periodic orbits. Analytical results are supported with the help of numerical simulations.