Bifurcations for a phytoplankton model with time delay

Abstract

Applying a frequency domain approach, we investigate a phytoplankton model with time delay. We use the delay as a bifurcation parameter; as it passes through a sequence of critical values, Hopf bifurcation occurs. A family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations illustrate our theoretical results.

Keywords

• Phytoplankton model
• Hopf bifurcation
• stability
• frequency domain
• Nyquist criterion