Neimark-Sacker bifurcation and stability analysis in a discrete phytoplankton-zooplankton system with Holling type II functional response

TL;DR

This paper analyzes a discrete phytoplankton-zooplankton model with Holling type II response, identifying bifurcation points and stability, revealing complex dynamics not seen in continuous models.

Contribution

It demonstrates the occurrence of Neimark-Sacker bifurcation and stability conditions in a discrete phytoplankton-zooplankton system with Holling type II response, providing new insights into its dynamics.

Findings

Neimark-Sacker bifurcation occurs at positive fixed points.

Positive fixed points are proven to be locally stable under certain conditions.

The system exhibits complex dynamics not present in continuous models.

Abstract

In this paper, we study discrete-time model of phytoplankton-zooplankton with Holling type II predator functional response. It is shown that Neimark-Sacker bifurcation occurs at the one of positive fixed points for certain parameter chosen as a bifurcation parameter. The existence and local stability of the positive fixed points of the model are proved. By considering theoretical results in the concrete example, it was obtained interesting dynamics of this system, which is not investigated in its corresponding continuous system.