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 Concept Videos

Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

134
Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...
134
First Order Systems01:21

First Order Systems

527
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
527
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

851
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
851
Application of Integration: Problem Solving01:30

Application of Integration: Problem Solving

211
The process of breathing involves the periodic intake and expulsion of air, known as the respiratory cycle, which typically lasts about five seconds. Modeling the volume of air inhaled into the lungs as a function of time provides insight into both the dynamics and efficiency of pulmonary ventilation. This volume is determined by integrating the airflow rate over time, which captures the cumulative effect of air entering the lungs.Sinusoidal Model of AirflowAirflow during respiration is not...
211
Properties of Laplace Transform-II01:16

Properties of Laplace Transform-II

686
Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
686
Integration of Synaptic Events01:28

Integration of Synaptic Events

6.5K
Synaptic integration mainly includes the summation of graded potentials. Graded potentials, regardless of their type, cause subtle alterations in membrane voltage, resulting in either depolarization or hyperpolarization. These incremental changes, when combined or summed, can propel the neuron toward its threshold. Consider, for example, a membrane experiencing a +15 mV shift, causing it to depolarize from -70 mV to -55 mV. In this scenario, graded potentials govern the membrane's ability to...
6.5K

You might also read

Related Articles

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

Sort by
Same author

[Bidirectional links between sleep deprivation and neurodegenerative diseases].

Zhurnal nevrologii i psikhiatrii imeni S.S. Korsakova·2026
Same author

Explainable AI for analyzing the decision of GNNs at predicting dynamic stability of complex oscillator networks.

Chaos (Woodbury, N.Y.)·2025
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

[Sleep deprivation and the development of oxidative stress in animal models].

Zhurnal nevrologii i psikhiatrii imeni S.S. Korsakova·2025
Same author

Canard Cascading in Networks with Adaptive Mean-Field Coupling.

Physical review letters·2024
Same author

Description and Genomic Analysis of the First Facultatively Lithoautotrophic, Thermophilic Bacteria of the Genus Thermaerobacter Isolated from Low-temperature Sediments of Lake Baikal.

Microbial ecology·2023
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
Same journal

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

Chaos (Woodbury, N.Y.)·2026
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Apr 18, 2026

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses
08:34

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Published on: May 9, 2021

3.2K

Quantifying chaotic dynamics from integrate-and-fire processes.

A N Pavlov1, O N Pavlova1, Y K Mohammad1

  • 1Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia.

Chaos (Woodbury, N.Y.)
|February 2, 2015
PubMed
Summary
This summary is machine-generated.

Estimating chaotic dynamics from low-rate neural firing (ISI) is challenging. This study improves Lyapunov exponent (LE) calculation from integrate-and-fire (IF) models, enabling better analysis of complex neural oscillations.

More Related Videos

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
16:01

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures

Published on: August 1, 2011

27.1K
Confocal Laser Scanning Microscopy of Calcium Dynamics in Acute Mouse Pancreatic Tissue Slices
10:49

Confocal Laser Scanning Microscopy of Calcium Dynamics in Acute Mouse Pancreatic Tissue Slices

Published on: April 13, 2021

5.1K

Related Experiment Videos

Last Updated: Apr 18, 2026

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses
08:34

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Published on: May 9, 2021

3.2K
Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
16:01

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures

Published on: August 1, 2011

27.1K
Confocal Laser Scanning Microscopy of Calcium Dynamics in Acute Mouse Pancreatic Tissue Slices
10:49

Confocal Laser Scanning Microscopy of Calcium Dynamics in Acute Mouse Pancreatic Tissue Slices

Published on: April 13, 2021

5.1K

Area of Science:

  • Computational Neuroscience
  • Nonlinear Dynamics
  • Signal Processing

Background:

  • Characterizing chaotic dynamics in neural systems is crucial for understanding brain function.
  • Interspike interval (ISI) sequences from integrate-and-fire (IF) models are common point processes.
  • Accurate estimation of Lyapunov exponents (LEs) is vital for quantifying chaotic dynamics.

Purpose of the Study:

  • To address the challenges in estimating Lyapunov exponents (LEs) from low-firing rate IF interspike interval (ISI) sequences.
  • To identify factors causing underestimation of LEs in IF models.
  • To propose and demonstrate an improved numerical method for determining LEs from IF ISI sequences.

Main Methods:

  • Analysis of dynamical features in IF ISI sequences.
  • Numerical determination of Lyapunov exponents (LEs).
  • Investigation of factors affecting LE estimation accuracy.

Main Results:

  • Low firing rates complicate accurate LE estimation in IF models.
  • Identified key factors leading to underestimated LEs.
  • Demonstrated an improved method for numerical LE determination from IF ISI sequences.
  • Showed that LEs can be estimated with approximately 400 mean periods in phase-coherent chaos.

Conclusions:

  • Accurate quantification of chaotic dynamics from IF models at low firing rates requires refined methods.
  • The proposed method enhances the reliability of LE estimation.
  • This work provides a pathway for analyzing complex neural oscillations in real-world data.