Persistence and global attractivity of a nonlocal single phytoplankton species model in almost periodic environments

In this study, we consider a nonlocal almost periodic reaction–diffusion–advection model to study the global dynamics of a single phytoplankton population under the assumption that nutrients are abundant and their metabolism is only affected by light intensity. First, we prove that the single phytoplankton species model is strongly monotone with respect to the order induced by cone $X$. Second, we characterize the upper Lyapunov exponent ${\lambda }^{\ast }$ for a class of almost periodic reaction–diffusion–advection equations, and provide a numerical method to compute it. On this basis, we prove that ${\lambda }^{\ast }$ is the threshold parameter for studying the global dynamic behavior of the population model. Our results show that if ${\lambda }^{\ast }<0$, phytoplankton species will become extinct, and if ${\lambda }^{\ast }>0$, phytoplankton species will be uniformly persistent. Finally, we verified the above results using numerical simulations.