Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons

An ensemble of stochastic non-leaky 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 looses 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 phaselocked. 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 to calculate the limit behavior for large ensembles and characterize the phase transition analytically. These results may be extensible to pulse ...

• Type: Journal
• Year: 2007
• Where: NECO
• Authors: Andreas Kaltenbrunner, Vicenç Gómez, Vicente López
• Keywords: Coupling, Coupling Strengths, Critical Coupling, NECO 2007