Qualitative Dynamics of a Discrete Phytoplankton-Zooplankton System with Holling Type II Grazing and Type III Toxin Release

TL;DR

This paper analyzes a discrete phytoplankton-zooplankton model incorporating Holling type II grazing and type III toxin release, exploring stability, bifurcations, and control strategies to manage complex dynamics.

Contribution

It provides a detailed analysis of the existence and stability of fixed points, bifurcation conditions, and the effect of feedback control in a novel discrete ecological model.

Findings

Conditions for Neimark--Sacker bifurcation are established.

Feedback control can suppress complex oscillations.

Global stability of boundary equilibrium is demonstrated.

Abstract

We study the dynamics of a discrete phytoplankton-zooplankton model with Holling type~II grazing and Holling type~III toxin release. The existence and stability of positive fixed points are analyzed, and conditions for the occurrence of Neimark--Sacker bifurcation are established. We show how feedback control can suppress complex dynamics near bifurcation. Global stability of the boundary equilibrium is also discussed. Numerical simulations confirm the theoretical findings, illustrating the rich behavior of the model under varying parameters