Time Delay Inference for Nonlinear Ecological Dynamic System: a Mathematical Study

Abstract

In this paper, we consider a mathematical model of phytoplankton-zooplankton with ratio dependent functional response and shedding effect. The special effect of discrete time delay on the dynamics of the system is studied. The boundedness of solutions is verified using Gronwell’s inequality. At the positive stationary state, the local and global stabilities have been analyzed (without time delay) by using Routh-Hurwitz and Lyapunov theorems respectively. The threshold value of time delay parameter for Hopf-bifurcation is derived. The conditions for diffusion induced instability have been obtained.