Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Extracting dynamics from threshold-crossing interspike intervals: possibilities and limitations.

A N Pavlov1, O V Sosnovtseva, E Mosekilde

  • 1Department of Physics, Saratov State University, Russia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 14, 2000
PubMed
Summary

This study estimates chaotic attractor dynamics using interspike intervals. We demonstrate that the largest Lyapunov exponent can be reliably calculated from return times, even when trajectories do not cross the chosen threshold.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Phenomenon of adjustment of brain rhythm coordination in healthy adolescents and with traumatic brain injury: An important marker of post-traumatic brain restoration.

Chaos (Woodbury, N.Y.)·2025
Same author

Enhanced multiresolution wavelet analysis of complex dynamics in nonlinear systems.

Chaos (Woodbury, N.Y.)·2021
Same author

Extended detrended fluctuation analysis of electroencephalograms signals during sleep and the opening of the blood-brain barrier.

Chaos (Woodbury, N.Y.)·2020
Same author

Solitary states and solitary state chimera in neural networks.

Chaos (Woodbury, N.Y.)·2019
Same author

Synchronization of spiral wave patterns in two-layer 2D lattices of nonlocally coupled discrete oscillators.

Chaos (Woodbury, N.Y.)·2019
Same author

Forced synchronization of a multilayer heterogeneous network of chaotic maps in the chimera state mode.

Chaos (Woodbury, N.Y.)·2019

Area of Science:

  • Dynamical systems theory
  • Nonlinear dynamics
  • Chaos theory

Background:

  • Chaotic attractors are fundamental in understanding complex systems.
  • Estimating dynamical characteristics like Lyapunov exponents is crucial for characterizing chaos.
  • Traditional methods can be sensitive to computational parameters.

Purpose of the Study:

  • To estimate dynamical characteristics of chaotic attractors.
  • To investigate the influence of threshold level on numerical computations.
  • To develop a robust method for estimating the largest Lyapunov exponent.

Main Methods:

  • Analysis of threshold-crossing interspike intervals.
  • Utilizing sequences of return times to a secant plane.
  • Numerical computation of dynamical properties.

Related Experiment Videos

Main Results:

  • Dynamical characteristics of chaotic attractors can be estimated from interspike intervals.
  • The choice of threshold level impacts numerical results.
  • The largest Lyapunov exponent can be estimated from return times, even with incomplete trajectory crossings.

Conclusions:

  • The proposed method provides a viable approach for estimating chaotic attractor dynamics.
  • Robust estimation of the largest Lyapunov exponent is achievable under general conditions.
  • The method is resilient to certain limitations in phase space trajectory data.