Stability, Bifurcation, and Chaos Control in a Discrete-Time Phytoplankton-Zooplankton Model with Holling Type II and Type III Functional Responses

TL;DR

This paper analyzes the complex dynamics of a discrete-time phytoplankton-zooplankton model with mixed Holling Type II and III responses, identifying stability, bifurcations, and chaos control through theoretical and numerical methods.

Contribution

It introduces a novel discrete-time model combining Holling Type II and III responses and explores its stability and bifurcation behavior.

Findings

Identification of fixed points and their stability

Proof of Neimark-Sacker bifurcation occurrence

Numerical validation of theoretical results

Abstract

In this paper, we investigate the dynamics of a discrete-time phytoplankton-zooplankton model where the predator functional response and toxin distribution functions follow both Holling Type II and Holling Type III forms simultaneously. We analyze the types of fixed points and the global stability of the system. Additionally, we prove the occurrence of a Neimark-Sacker bifurcation at the positive fixed point. The theoretical findings are validated through numerical simulations