Patterns of interval correlations in neural oscillators with adaptation

Neural firing is often subject to negative feedback by adaptationcurrents. These currents can induce strong correlations among the timeintervals between spikes. Here we study analytically the intervalcorrelations of a broad class of noisy neural oscillators withspike-triggered adaptation of arbitrary strength and time scale. Ourweak-noise theory provides a general relation between the correlationsand the phase-response curve (PRC) of the oscillator, provesanti-correlations between neighboring intervals for adapting neuronswith type I PRC and identifies a single order parameter thatdetermines the qualitative pattern of correlations. Monotonicallydecaying or oscillating correlation structures can be related toqualitatively different voltage traces after spiking, which can beexplained by the phase plane geometry. At high firing rates, thelong-term variability of the spike train associated with thecumulative interval correlations becomes small, independent of modeldetails. Our results are verified by comparison with stochasticsimulations of the exponential, leaky, and generalizedintegrate-and-fire models with adaptation