Interactive Movement, Aggregation, and Swarm Dynamics

Abstract

We consider a general class of models for biological interactive movement describing collective phenomena such as chemotaxis and tensiotaxis of cells or swarming of birds. Using the joint name 'bimes' for such biological interacting and moving entities, we suppose that communication between 'bimes' is performed via a specific medium by establishing therein a dynamic interaction field, whose perception stimulates the dynamic response and motile activity of each single 'bime'. In some particular cases, sample simulations are shown for one and two spatial dimensions. We discuss how a proposed general modeling approach using Voronoi tessellation and Delaunay triangulation might help to formulate and simulate collective cell movement with direct cell-cell contact, as occurs in models for wound healing and other cell tissue dynamics.