Bifurcation and pattern dynamics in the nutrient-plankton network

Abstract

This paper used a Holling-IV nutrient-plankton model with a network to describe algae's spatial and temporal distribution and variation in a specific sea area. The stability and bifurcation of the nonlinear dynamic model of harmful algal blooms (HABs) were analyzed using the nonlinear dynamic theory and de-eutrophication's effect on algae's nonlinear dynamic behavior. The conditions for equilibrium points (local and global), saddle-node, transcritical, Hopf-Andronov and Bogdanov-Takens (B-T) bifurcation were obtained. The stability of the limit cycle was then judged and the rich and complex phenomenon was obtained by numerical simulations, which revealed the robustness of the nutrient-plankton system by switching between nodes. Also, these results show the relationship between HABs and bifurcation, which has important guiding significance for solving the environmental problems of HABs caused by the abnormal increase of phytoplankton.

Keywords

• patterns
• nutrient-plankton system
• bifurcation
• random network
• holling-iv functional response