Abstract -- Simple rules, when executed by individual agents in a large group, or swarm, can lead to complex behaviors that are often difficult or impossible to predict knowing only the rules. However, aggregate behavior is not always unpredictable—even for swarm models said to be beyond analysis. For the class of swarming algorithms examined herein, we analytically identify several possible emergent behaviors and their underlying causes: clustering, drifting, and explosion. They also analyze the likelihood of these behaviors emerging from randomly selected swarm configurations and present a few examples. The analytic results are illustrated via simulation

Abstract -- Abstract—Given simple agent rules, a swarm’s emergent behavior can be difficult to predict. The inverse problem is even more difficult: given a desired emergent behavior, what are the rules by which swarm agents should operate? Disjunctive fuzzy control is proposed as a method to model swarm agents. Compared to more commonly used conjunctive fuzzy control such as that proposed by Mamdami, disjunctive fuzzy control is robustly fault tolerant and disjointly connected. Instead of agents working in coordination with one another, each swarm agent contributes individually to the result. As is the case with social insect swarms, the emergent behavior displays gracious degradation as agents are lost. Disjunctive control allows adaptation of the describing membership function, as is commonly done in conjunctive control. The inversion process is illustrated with numerous examples,
including a predator-prey game, traffic control, gang warfare, and escaping agents. A number of behaviors emerged in each scenario showing the ability of swarminversion to discovering unexpected new strategies.