# Quantifying chaotic dynamics from integrate-and-fire processes

## 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.

- 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 integrate-and-fire 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 integrate-and-fire 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. Thu .
"Quantifying chaotic dynamics from integrate-and-fire processes". United States.
doi:10.1063/1.4907175.
```

```
@article{osti_22402528,
```

title = {Quantifying chaotic dynamics from integrate-and-fire 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 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.},

doi = {10.1063/1.4907175},

journal = {Chaos (Woodbury, N. Y.)},

number = 1,

volume = 25,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}