Stability and Bifurcation in a Discrete Phytoplankton-Zooplankton Model with Holling-Type Toxic Effects

TL;DR

This paper analyzes a discrete phytoplankton-zooplankton model with Holling-type toxin effects, deriving stability conditions, classifying fixed points, and demonstrating bifurcations through theoretical analysis and numerical simulations.

Contribution

It introduces a novel discrete model incorporating Holling-type toxin effects and provides comprehensive stability and bifurcation analysis.

Findings

Existence of positive fixed points under certain conditions

Global stability of fixed points established

Neimark-Sacker bifurcation demonstrated

Abstract

In this paper, we investigate a discrete-time phytoplankton-zooplankton model that incorporates a linear predator functional response alongside a Holling-type toxin distribution. Both Holling type II and type III cases are considered, and we derive conditions on the model parameters that guarantee the existence of positive fixed points. We classify all fixed points and analyze their global stability. Furthermore, we establish the occurrence of a Neimark-Sacker bifurcation at the positive fixed point. Theoretical results are supported by numerical simulations, which illustrate the dynamic behavior of the system