We studied a plankton community composed of phytoplankton (prey) and zooplankton (predators) with herd-taxis. The herd-taxis implies that the zooplankton would not only trend towards the higher density zone of phytoplankton but also has conformity behavior, which leads to the nonlinear cross-diffusion. The stability analysis gives out the conditions for the Hopf stability and the Turing bifurcation. In addition, the active foraging behavior of zooplankton helps to spatially stabilize the algal system and contributes to smoothing the inhomogeneous distribution of plankton, which is in line with the economic common sense: an invisible hand regulates and balances the distribution of plankton. Then we employed the weakly nonlinear analysis to establish amplitude equations to explore the effect of herd-taxis on the self-organization and found three types of patterns: spot patterns, stripe patterns, mixed patterns of the spots and stripes. The numerical simulations validated the self-organization behaviors and helped us better understand the interactions in plankton communities in the real world.

我们研究了一个由浮游植物（猎物）和浮游动物（捕食者）组成的浮游生物群落。群居性意味着浮游动物不仅会趋向于浮游植物的高密度区，而且还具有整合行为，从而导致非线性交叉扩散。稳定性分析给出了 Hopf 稳定性和图灵分岔的条件。此外，浮游动物的主动觅食行为有助于在空间上稳定藻类系统，有助于平滑浮游生物的不均匀分布，这符合经济常识：一只看不见的手调节和平衡浮游生物的分布。然后我们采用弱非线性分析建立振幅方程来探讨从众出租车对自组织的影响，发现三种模式：斑点模式、条纹模式、斑点和条纹的混合模式。数值模拟验证了自组织行为，并帮助我们更好地了解现实世界中浮游生物群落的相互作用。