Dynamical Analysis of an Allelopathic Phytoplankton Model with Fear Effect

TL;DR

This paper introduces a novel phytoplankton competition model incorporating a fear effect and allelopathy, revealing complex dynamics and implications for species conservation through theoretical analysis and numerical simulations.

Contribution

It is the first to model allelopathic phytoplankton competition with a fear effect, analyzing its rich dynamics and spatial extensions.

Findings

Fear effect and allelopathy induce complex bifurcations.

Fear of toxic species leads to non-toxic species extinction.

Model results inform biodiversity conservation strategies.

Abstract

This paper is the first to propose an allelopathic phytoplankton competition ODE model influenced by a fear effect based on natural biological phenomena. It is shown that the interplay of this fear effect and the allelopathic term cause rich dynamics in the proposed competition model, such as global stability, transcritical bifurcation, pitchfork bifurcation, and saddle-node bifurcation. We also consider the spatially explicit version of the model and prove analogous results. Numerical simulations verify the feasibility of the theoretical analysis. The results demonstrate that the primary cause of the extinction of non-toxic species is the fear of toxic species compared to toxins. Allelopathy only affects the density of non-toxic species. The discussion provides guidance for the conservation of species and the maintenance of biodiversity.