Threshold dynamics of a periodic stoichiometric model

Abstract

In this paper, we investigate a general time-periodic stoichiometric ODE model, which describes the algal growth. The model system has singularities induced by the zero nitrogen concentration. We first observe that there exists a threshold value $ \lambda_0 $, which is exactly the principal eigenvalue of a nonlinear eigenvalue problem associated with a homogeneous of degree one system, and further show the global dynamics of the model system in terms of $ \lambda_0 $. In particular, we obtain the uniqueness of the positive periodic solution when $ \lambda_0>0 $. Finally, we carry out simulations to illustrate the analytic results.