Effect of herd-taxis on the self-organization of a plankton community

Abstract 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.