Quantifying chaotic dynamics from integrate-and-fire processes

A N Pavlov; O N Pavlova; Y K Mohammad; J Kurths

doi:10.1063/1.4907175

Quantifying chaotic dynamics from integrate-and-fire processes

Chaos. 2015 Jan;25(1):013118. doi: 10.1063/1.4907175.

Authors

A N Pavlov¹, O N Pavlova¹, Y K Mohammad¹, J Kurths²

Affiliations

¹ Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia.
² Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany.

PMID: 25637929
DOI: 10.1063/1.4907175

Abstract

Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.