Quantifying chaotic dynamics from integrateandfire processes
Abstract
Characterizing chaotic dynamics from integrateandfire (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 phasecoherent chaos. Application to real data is discussed.
 Authors:
 Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation)
 (Russian Federation)
 (Iraq)
 Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam (Germany)
 (Germany)
 Publication Date:
 OSTI Identifier:
 22402528
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DYNAMICS; FIRES; LYAPUNOV METHOD; OSCILLATIONS
Citation Formats
Pavlov, A. N., Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov, Pavlova, O. N., Mohammad, Y. K., Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit, Kurths, J., and Institute of Physics, Humboldt University Berlin, 12489 Berlin. Quantifying chaotic dynamics from integrateandfire processes. United States: N. p., 2015.
Web. doi:10.1063/1.4907175.
Pavlov, A. N., Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov, Pavlova, O. N., Mohammad, Y. K., Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit, Kurths, J., & Institute of Physics, Humboldt University Berlin, 12489 Berlin. Quantifying chaotic dynamics from integrateandfire processes. United States. doi:10.1063/1.4907175.
Pavlov, A. N., Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov, Pavlova, O. N., Mohammad, Y. K., Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit, Kurths, J., and Institute of Physics, Humboldt University Berlin, 12489 Berlin. 2015.
"Quantifying chaotic dynamics from integrateandfire processes". United States.
doi:10.1063/1.4907175.
@article{osti_22402528,
title = {Quantifying chaotic dynamics from integrateandfire processes},
author = {Pavlov, A. N. and Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov and Pavlova, O. N. and Mohammad, Y. K. and Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit and Kurths, J. and Institute of Physics, Humboldt University Berlin, 12489 Berlin},
abstractNote = {Characterizing chaotic dynamics from integrateandfire (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 phasecoherent chaos. Application to real data is discussed.},
doi = {10.1063/1.4907175},
journal = {Chaos (Woodbury, N. Y.)},
number = 1,
volume = 25,
place = {United States},
year = 2015,
month = 1
}

The dynamics of the standard integratefire model and a simpler model (that reproduces the important features of the integratefire model under certain conditions) of neural dynamics are studied in the presence of a deterministic external driving force, taken to be timeperiodic, and white background noise. Both models possess resonant phenomena in the first passage probability distribution and mean first passage time, arising from the interplay of characteristic time scales in the system. {copyright} {ital 1996 The American Physical Society.}

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