Hopf Bifurcation Analysis of a Diffusive Nutrient–Phytoplankton Model with Time Delay

Abstract

In this paper, we studied a nutrient–phytoplankton model with time delay and diffusion term. We studied the Turing instability, local stability, and the existence of Hopf bifurcation. Some formulas are obtained to determine the direction of the bifurcation and the stability of periodic solutions by the central manifold theory and normal form method. Finally, we verify the above conclusion through numerical simulation.

Editorial: Overview and Some New Directions

“…Considering the importance of the nutrient-phytoplankton, in reference [8], Ruizhi Yang, Liye Wang and Dan Jin consider Hopf bifurcation analysis of a diffusive nutrientphytoplankton model with time delay. One of the most complex and difficult problems in water pollution treatment is the prevention and control of algal bloom.…”