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Center for Nonlinear Studies |
We are interested in exploring collective variables of brain function. Specifically we show that the development of synchrony in a biologically inspired network of integrate-and-fire neurons can realize the computation of recognizing patterns in sensory stimuli. We then focus on the principles underlying the development of this synchrony in neuron spike times from the perspective of a dynamical phase transition. The frustration due to the interplay between a neuron's natural firing period and the collective input from the rest of the network, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics controlled by a correlation time that can diverge at phase boundaries. A model-independent description developed in terms of the theory of circle maps leads to two classes of continuous phase transitions -- one of which does not involve a diverging scale.
Host: Krastan Blagoev, T-10