The Effect of Herd-Taxis

In this chapter, the herd-taxi is considered for a plankton community composed of phytoplankton (prey) and zooplankton (predators) because that the herd-taxis indicates the effect of the zooplankton on the higher density zone of phytoplankton and generation of the conformity behavior leading to the nonlinear cross-diffusion phenomena. We use the stability analysis to get the conditions of the Hopf stability and the Turing bifurcation. Moreover, the active foraging behavior of zooplankton plays important role in spatially stabilizing the algal system and smoothing the inhomogeneous distribution of plankton. Significantly, it is also in line with the economic basic idea that there exists an invisible hand regulating and balancing the distribution of plankton. In addition, the weakly nonlinear analysis is employed to establish amplitude equations in order to explore the effect of herd-taxis on the self-organization. Successfully, three types of patterns are found out such as spot patterns, stripe patterns, and mixed patterns of the spots and stripes. There also present some numerical simulations to validate the self-organization behaviors and help us further understand the interactions in plankton communities in the real world.