Dynamical Analysis of Toxin Producing Model with Delay

Abstract:

      In this paper, a toxin producing phytoplankton-zooplankton model with inhibitory substrate and time delay is investigated. A discrete time delay is induced to both of the consume response function and distribution of toxic substance term. Moreover, Tissiet type function is used for zooplankton grazing to account for the effect of toxication by the TPP population. The conditions to guarantee the coexistence of two species and stability of coexistence equilibrium are given. In particular, we show that there exist critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when the delay parameters cross their critical values. Some numerical simulations are executed to validate the analytical findings.