The Global Dynamics Of A Single Phytoplankton Species Model In Almost Periodic Environments

Since phytoplankton play an important role in the global ecosystem,it is very important to understand the global dynamics of phytoplankton model in order to propose effective measures to control the growth of phytoplankton population.In this paper,we consider two kinds of nonlocal almost periodic reaction diffusion advection models to study the global dynamics of a single phytoplankton population under the assumption that nutrients are sufficient and metabolism is only affected by light intensity.Firstly,we consider a reaction-diffusion-advection model in which the diffusion coefficient and advection coefficient are constant and the nonlinear term is an uniformly almost periodic function.By using the comparison principle of generalized super-and sub-solutions,we give the definition of upper Lyapunov exponent and prove the global dynamic behavior of the species model with λ~* as the threshold,if λ~*<0,the phytoplankton species will extinct,and if λ~*>0,the phytoplankton species will uniformly persistent.Secondly,the reaction-diffusion-advection model in which diffusion coefficient,advection coefficient and nonlinear term are almost periodic functions.Similarly,in terms of the comparison principle of generalized super-and sub-solutions,we give the definition of upper Lyapunov exponent,and prove that λ~* is the threshold parameter to study the global dynamics behavior of the population model.Finally,by using numerical method of upper Lyapunov exponent given in this paper,we verify the above results by virtue of numerical simulations.