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

Linear time-invariant Systems01:23

Linear time-invariant Systems

832
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
832
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

328
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
328
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

310
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
310
Classification of Systems-II01:31

Classification of Systems-II

442
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
442
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

609
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
609
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

464
A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
464

You might also read

Related Articles

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

Sort by
Same author

Wafer-scale CMOS foundry silicon-on-insulator devices for integrated temporal pulse compression.

Nanophotonics (Berlin, Germany)·2025
Same author

Immunoglobulin gene expression profiles and microbiome characteristics in periodontitis in nonhuman primates.

Molecular immunology·2022
Same author

Variations in temporal trends in non-traumatic dental condition related emergencies.

Journal of public health dentistry·2022
Same author

Oral Microbiome and Gingival Gene Expression of Inflammatory Biomolecules With Aging and Periodontitis.

Frontiers in oral health·2022
Same author

Transcriptomic phases of periodontitis lesions using the nonhuman primate model.

Scientific reports·2021
Same author

Variations in Schedule III prescription patterns in a Medicaid population pre- and post-policy.

Scientific reports·2021

Related Experiment Video

Updated: Jan 6, 2026

Photodiode-Based Optical Imaging for Recording Network Dynamics with Single-Neuron Resolution in Non-Transgenic Invertebrates
10:18

Photodiode-Based Optical Imaging for Recording Network Dynamics with Single-Neuron Resolution in Non-Transgenic Invertebrates

Published on: July 9, 2020

3.3K

Deciphering Dynamical Nonlinearities in Short Time Series Using Recurrent Neural Networks.

Radhakrishnan Nagarajan1

  • 1Center for Oral and Systemic Health, Marshfield Clinic Research Institute, 1000 North Oak Avenue, Marshfield, WI, 54449, USA. nagarajanr@marshfieldresearch.org.

Scientific Reports
|October 4, 2019
PubMed
Summary

This study introduces a novel recurrent neural network framework to detect dynamical nonlinearities in short time series. The method accurately identifies chaotic processes, outperforming traditional statistical tests.

Related Experiment Videos

Last Updated: Jan 6, 2026

Photodiode-Based Optical Imaging for Recording Network Dynamics with Single-Neuron Resolution in Non-Transgenic Invertebrates
10:18

Photodiode-Based Optical Imaging for Recording Network Dynamics with Single-Neuron Resolution in Non-Transgenic Invertebrates

Published on: July 9, 2020

3.3K

Area of Science:

  • Dynamical Systems
  • Nonlinear Dynamics
  • Time Series Analysis

Background:

  • Surrogate testing is widely used to detect dynamical nonlinearities in chaotic processes.
  • Traditional methods rely on statistical hypothesis testing and discriminant statistics, which are challenging for short time series.
  • Existing methods have limitations in generalizability due to reliance on single empirical samples.

Purpose of the Study:

  • To propose a recurrent neural network (RNN) classification framework for identifying dynamical nonlinearities.
  • To overcome limitations of traditional surrogate testing, particularly with short time series.
  • To enhance the generalizability of findings by accommodating multiple time series realizations.

Main Methods:

  • A recurrent neural network classification framework was developed.
  • The framework utilizes raw time series data, eliminating the need for discriminant statistics.
  • The method was tested on short time series (L=32, 64, 128) from various dynamical systems and data types.

Main Results:

  • The RNN classifier achieved accuracy significantly higher than 50% for processes in chaotic regimes.
  • Performance on nonlinearly correlated noise was around 50%, comparable to random chance.
  • The framework demonstrated effectiveness on continuous and discrete dynamical systems, nonlinear transformations, and experimental data.

Conclusions:

  • The proposed RNN framework is effective in identifying dynamical nonlinearities from short time series.
  • This approach offers improved generalizability and obviates the need for complex discriminant statistics.
  • The findings highlight the potential of deep learning for analyzing complex dynamical systems.