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(Neural Computation. 2007;19:3011-3050.)
© 2007 The MIT Press

Letter

Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons

Andreas Kaltenbrunner

andreas.kaltenbrunner{at}upf.edu Universitat Pompeu Fabra, Departament de Tecnologia, 08003 Barcelona, Spain, and Barcelona Media Centre d'Innovació, 08003 Barcelona, Spain

Vicenç Gómez

vgomez{at}iua.upf.edu Universitat Pompeu Fabra, Departament de Tecnologia, 08003 Barcelona, Spain, and Barcelona Media Centre d'Innovació, 08003 Barcelona, Spain

Vicente López

vicente.lopez{at}upf.edu Universitat Pompeu Fabra, Departament de Tecnologia, 08003 Barcelona, Spain, and Barcelona Media Centre d'Innovació, 08003 Barcelona, Spain

An ensemble of stochastic nonleaky integrate-and-fire neurons with global, delayed, and excitatory coupling and a small refractory period is analyzed. Simulations with adiabatic changes of the coupling strength indicate the presence of a phase transition accompanied by a hysteresis around a critical coupling strength. Below the critical coupling production of spikes in the ensemble is governed by the stochastic dynamics, whereas for coupling greater than the critical value, the stochastic dynamics loses its influence and the units organize into several clusters with self-sustained activity. All units within one cluster spike in unison, and the clusters themselves are phase-locked. Theoretical analysis leads to upper and lower bounds for the average interspike interval of the ensemble valid for all possible coupling strengths. The bounds allow calculating the limit behavior for large ensembles and characterize the phase transition analytically. These results may be extensible to pulse-coupled oscillators.






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