Bifurcations of a discrete-time Phytoplankton-Zooplankton model

Volume 8, Issue 5, October 2023     |     PP. 139-174      |     PDF (1929 K)    |     Pub. Date: October 30, 2023
DOI: 10.54647/mathematics110427    79 Downloads     162832 Views  

Author(s)

Vimbiso Shiri, Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
Xianyi Li, Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

Abstract
This work mainly investigates the bifurcation problems and topological classifications of a discrete phytoplankton-zooplankton model, whose continuous version was proposed by Truscott and Brindley in 1994. The model is derived by using the semi-discretization technique. Within this study, trivial and semi-trivial fixed points are identified, as well as an interior fixed point that emerges based on specific parametric conditions. Subsequently, an exploration of their topological classifications is undertaken, employing linear stability theory in the vicinity of the trivial, semi-trivial, and interior fixed points. Leveraging the center manifold theorem and bifurcation theory, it is feasible to derive conditions under which the flip and Neimark-Sacker bifurcations are expected to transpire. To validate these findings and draw conclusions, numerical simulations are conducted which produce proof of a Neimark-Sacker bifurcation. Through these comprehensive analyses and simulations, the main aim of this research is to effectively augment the understanding of the dynamics of the model and affirm the validity of our results.

Keywords
Phytoplankton-zooplankton model, semi-discretization, flip bifurcation, Neimark-Sacker bifurcation.

Cite this paper
Vimbiso Shiri, Xianyi Li, Bifurcations of a discrete-time Phytoplankton-Zooplankton model , SCIREA Journal of Mathematics. Volume 8, Issue 5, October 2023 | PP. 139-174. 10.54647/mathematics110427

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