Bifurcation analysis of solutions to a nonlocal phytoplankton model under photoinhibition

Yuan-Yuan Zhou

doi:10.3934/dcdsb.2022104

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2023, Volume 28, Issue 2: 909-919. Doi: 10.3934/dcdsb.2022104

This issue Previous Article Global attractor for a partly dissipative reaction-diffusion system with discontinuous nonlinearity Next Article Stability in the energy space of the sum of

$ N $

solitary waves for an equation modelling shallow water waves of moderate amplitude

Bifurcation analysis of solutions to a nonlocal phytoplankton model under photoinhibition

Yuan-Yuan Zhou

School of Mathematics, Hunan University, Changsha 410082, China

Received: September 30, 2021

Revised: March 31, 2022

Early access: June 2022

Published: February 2023

Yuan-Yuan Zhou is supported by NSFC No. 12171143

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Abstract

We investigate the effect of photoinhibition in a nonlocal reaction-diffusion-advection equation, which models the dynamics of a single phytoplankton species in a water column where the growth of the species depends solely on light. First, for $ k_0 = 0 $, we proved that system (1)-(3) forms a strongly monotone dynamical system with respect to a non-standard cone related to the cumulative distribution function. Second, local and global bifurcation theory are used to show that the model with photoinhibition possesses multiple steady-states with the change of parameter ranges.

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Mathematics Subject Classification: Primary: 35k57, 92D25; Secondary: 35B51.

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