Hopf-transcritical bifurcation in toxic phytoplankton–zooplankton model with delay

• DOI: 10.1016/j.jmaa.2014.01.081
• Publication Date: 2014-02-03T18:32:01Z
• Authors: Yong Wang; Hongbin Wang; Weihua Jiang
• Keywords: Transcritical bifurcation; Center manifold; Pitchfork bifurcation

In this paper, a phytoplankton–zooplankton model with toxic liberation delay is considered. Firstly, the critical values of Hopf bifurcation, transcritical bifurcation and Hopf-transcritical are given, to give more detailed information about periodic oscillations, direction stability studied by using normal-form theory center manifold theorem. Then, we set calculating universal unfoldings near point. Finally, show that plankton system may exhibit quasi-periodic which verified both theoretically numerically, explain experimental observed fluctuation phenomenon population.