A mathematical model for the dynamics of clustering

摘要: Abstract The formation of several clusters, arising from attracting forces between nonidentical entities or agents, is a phenomenon observed in diverse fields. Think people gathered through mutual interest, swarm behaviour animals clustering oscillators brain cells. We introduce dynamic model mutually agents for which we prove that the long-term consists organized into groups clusters. have completely characterized cluster structure (i.e. the number clusters and their composition) by means set inequalities parameters identified intensity attraction as key parameter governing transition different structures. versatility will be illustrated discussing its relation to Kuramoto describing how it applies system interconnected water basins.