Stability and Hopf bifurcation analysis of a nutrient-phytoplankton model with delay effect. (English) Zbl 1470.37114

Summary: A delay differential system is investigated based on a previously proposed nutrient-phytoplankton model. The time delay is regarded as a bifurcation parameter. Our aim is to determine how the time delay affects the system. First, we study the existence and local stability of two equilibria using the characteristic equation and identify the condition where a Hopf bifurcation can occur. Second, the formulae that determine the direction of the Hopf bifurcation and the stability of periodic solutions are obtained using the normal form and the center manifold theory. Furthermore, our main results are illustrated using numerical simulations.


37N25 Dynamical systems in biology
92D25 Population dynamics (general)
35B32 Bifurcations in context of PDEs
35B35 Stability in context of PDEs
Full Text: DOI


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