Bifurcation analysis of solutions to a nonlocal phytoplankton model under photoinhibition

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ k_0 = 0 $\end{document}</tex-math></inline-formula>, 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.</p>