Department of Applied Mathematics, National University of Kaohsiung
The phenomena of collective motions such as flocking of birds, schooling of fish and swarming of bacteria are often observed in complex biological systems. Among many models for investigating the above mentioned systems, the one introduced by Cucker and Smale has quickly attracted much attention. In this talk, we will discuss the flocking motion on the discrete-time Cucker-Smale model in which agents having their free-will accelerations. We prove theoretically that if the free-will accelerations of agents are summable, then the flocking motion occurs by letting the strength of the interaction between agents strong enough. Some numerical simulations to support our theoretical results will also be presented. This is a joint work with Prof. Jonq Juang.