Research on stability and Hopf bifurcation of marine ecosystem dynamics models

The predictability of marine ecosystem dynamics models is one of the most vital factors to limit their practical applications, of which the stability is the fundamental condition. In order to discuss the stability and Hopf bifurcation of marine ecosystem dynamics models, an approach based on a theorem termed dimension reduction was proposed and further applied in the mass-conservative nutrient-phytoplankton-zooplankton-detritus（NPZD） model in this paper. Results showed that the nonsingular equilibrium point of NPZD model was analytically stable in use of the dimension reduction theorem and the Hopf bifurcation might occur when model parameters changed along the threshold values. The analytical results of the NPZD model were further verified by numerical simulation in this study. It can be concluded that this approach based on the dimension reduction theorem is well applicable to the theoretical analysis of a kind of stability problems and Hopf bifurcation of massconservative systems.