Sequential Desynchronization in Networks of Spiking Neurons with Partial Reset

Abstract

The response of a neuron to synaptic input strongly depends on whether or not it has just emitted a spike. We propose a neuron model that after spike emission exhibits a partial response to residual input charges and study its collective network dynamics analytically. We uncover a novel desynchronization mechanism that causes a sequential desynchronization transition: In globally coupled neurons an increase in the strength of the partial response induces a sequence of bifurcations from states with large clusters of synchronously firing neurons, through states with smaller clusters to completely asynchronous spiking. We briefly discuss key consequences of this mechanism for more general networks of biophysical neurons.

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• Stability of splay states in globally coupled rotators
• Chaos and correlated avalanches in excitatory neural networks with synaptic plasticity
• Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators
• Transition to complete synchronization and global intermittent synchronization in an array of time-delay systems
• Order symmetry breaking and broad distribution of events in spiking neural networks with continuous membrane potential
• Partially unstable attractors in networks of forced integrate-and-fire oscillators
• Transient dynamics of pulse-coupled oscillators with nonlinear charging curves
• Stochastic facilitation in heteroclinic communication channels
• Statistics of spike trains in conductance-based neural networks: Rigorous results
• Percolation critical exponents in cluster kinetics of pulse-coupled oscillators