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Stochastic Phase Decoupling in Random Graphical Dynamical Systems

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William Sulis, Collective Intelligence Laboratory , McMaster University,
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Random graphical dynamical systems (RGDS) generalize the usual random graph (RG)model by allowing dynamic connections between agents. Previous work has shown that many RG phase transitions carry over to RGDS when one weakens the notion of phase transition to that of a stochastic phase transition (a qualitative change in a probability distribution over some order parameter). The connection rule of the holding time model, in which a network of agents randomly form connections up to a indidivual degree (sociability) and maintain these connections for an individual duration (holding time), has been modified to permit the selection of connections based upon two properties of the agents - sociability and trait. Stochastic phase transitions appear for an order parameter (n-f bias) defined for trait and for sociability. When the dynamics of connections involves a weak coupling between sociability and trait, the respective stochastic phase transitions become decoupled. This phenomenon may be relevant in situation of horizontal emergence.