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Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems by proving that the governing equations are generated by(More)
Transitions between dynamical states in integrate-and-fire neuron models with periodic stimuli result from tangent or discontinuous bifurcations of a return map. We study their characteristic scaling laws and show that discontinuous bifurcations exhibit a kind of phase transition intermediate between continuous and first order. In the model-independent(More)
We investigate extensions to the model put forward by Brody and Hopfield [1] for spike-timing based pattern recognition applied to mammalian olfaction. Their model implements a pattern recognition algorithm realized in the dynamics of a network of coupled IF neurons subject to a sine-wave rhythm. Subsets of these neurons can synchronize through the(More)
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of(More)
We develop an analytic framework to investigate the stability of splay states in infinite networks of identical integrate-and-fire neurons coupled through synaptic pulses. More specifically we perform a linear stability analysis of the splay state probability distribution whose dynamics is governed by an appropriate Fokker Planck equation. For exponentially(More)
We explore patterns in the spike timing of neurons receiving periodic inputs, with an emphasis on stable characteristics which are realized in both models and in-vitro whole-cell recordings. We report on whole-cell recordings of pyramidal CA1 cells from rat hippocampus and entorhinal cortex and compare this data to model simulations. Cells were injected(More)
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