Firing-rate, symbolic dynamics and frequency dependence in periodically driven spiking models: a piecewise-smooth approach

Research output: Contribution to journalJournal article – Annual report year: 2015Researchpeer-review

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In this work we consider a periodically forced generic integrate-and-fire model with a unique attracting equilibrium in the subthreshold dynamics and study the dependence of the firing-rate on the frequency of the drive. In an earlier study we have obtained rigorous results on the bifurcation structure in such systems, with emphasis on the relation between the firing-rate and the rotation number of the existing periodic orbits. In this work we study how these bifurcation structures behave upon variation of the frequency of the input. This allows us to show that the dependence of the firing-rate on frequency of the drive follows a devil's staircase with non-monotonic steps and that there is an optimal response in the whole frequency domain. We also characterize certain bounded frequency windows in which the firing-rate exhibits a bell-shaped envelope with a global maximum.
Original languageEnglish
Issue number5
Pages (from-to)1163-1192
Publication statusPublished - 2015
Externally publishedYes
CitationsWeb of Science® Times Cited: No match on DOI

    Research areas

  • Firing-rate, Integrate-and-fire, Piecewise-smooth, Period adding, Border collision bifurcations

ID: 118437878