Mathematical Modeling of Collective Behavior in Physical and Social Systems

In this paper, we examine the phenomenon of collective behavior as it broadly reveals itself in different living and nonliving systems. It has previously been argued that self-organizing behavior that occurs in dissipative systems resembles the kind of collective behavior that is seen in living systems. In this paper, we specifically discuss the evolution of collective behavior, i.e., how a system learns as it engages in a collective, self-organizing activity over time. We specifically look at this phenomenon through the examples of Futbol and chemical flocking of a benzoquinone system, which reveal common patterns of learning that occur in a collective setting. The growth profile of the examples studied reveal the existence of criticality and phase transition which are fundamental traits of such complex systems.