Complex pattern dynamics and synchronization in a coupled spatiotemporal plankton system with zooplankton vertical migration

Abstract

In aquatic environments, zooplankton often exhibits life habit of vertical migration and the phytoplankton-zooplankton predator-prey systems in different water layers are therefore coupled together. To uncover the nonlinear mechanisms of pattern dynamics in such coupled plankton system, a spatiotemporal model is developed in this research with the consideration of plankton horizontal diffusion and zooplankton vertical migration. Equation of dispersion curve for the coupled system is derived, and an extension of regular Turing instability is disclosed by determining the number of peaks on the dispersion curve. We find a mechanism named as “projection of characteristics” that local or global characteristics projecting between different subsystems causes the self-organization of complex patterns with multi-scale structures. The combination of various bifurcations with Turing instability controls the system stability and can lead to more complex pattern formation. Notably, when flip bifurcation takes place, the coupled system generates an interesting result that the phytoplankton populations in some water layers become extinct but the zooplankton populations in these layers can still be persistent due to the effect of population compensation. It is also found that the increase of zooplankton migration rate can result to spatiotemporal synchronization of pattern evolution, and that particularly, the pattern dynamics in just a part of subsystems achieve local synchronization. The methods and results presented herein may lead to a better understanding on the emergence of complex plankton patchiness in nature.