Modeling alignment and movement of animals and cells

Abstract

Schools of fish and flocks of birds are examples for groups of individuals moving in a highly organized way. Individuals adapt their orientation and speed to that of their (nearest) neighbors. Adaptation of orientation can also be found on the cellular and subcellular level and is called alignment. A model for alignment and movement is derived on the basis of reaction transport equations in one space dimension. Existence of solutions is shown and long time behavior of the system is described. The effect of schooling on the risk of predation is investigated. Then the model is generalized to two space dimensions and compared to other models for alignment which do not incorporate individual movement in space.