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

Transversal homoclinic orbits in a transiently chaotic neural network.

Shyan-Shiou Chen1, Chih-Wen Shih

  • 1Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Republic of China.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary
This summary is machine-generated.

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

Stoichiometric balance and sustained rhythms.

Journal of mathematical biology·2026
Same author

Collective Oscillations in Coupled-Cell Systems.

Bulletin of mathematical biology·2021
Same author

On an age structured population model with density-dependent dispersals between two patches.

Mathematical biosciences and engineering : MBE·2019
Same author

Within-Host Viral Dynamics in a Multi-compartmental Environment.

Bulletin of mathematical biology·2019
Same author

Coexistence and extinction for two competing species in patchy environments.

Mathematical biosciences and engineering : MBE·2019
Same author

The kinetics in mathematical models on segmentation clock genes in zebrafish.

Journal of mathematical biology·2017

This study confirms transient chaos in discrete-time neural networks by identifying snap-back repellers. This finding is crucial for understanding chaotic dynamics and optimizing combinatorial problems.

Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Artificial Neural Networks

Background:

  • Discrete-time neural networks can exhibit complex dynamics.
  • Transient chaos, characterized by temporary chaotic behavior, is a key phenomenon in dynamical systems.
  • Understanding chaotic dynamics is essential for applications like optimization.

Purpose of the Study:

  • To investigate the existence of snap-back repellers in discrete-time neural networks.
  • To establish the conditions for chaotic behaviors (Li-Yorke or Marotto chaos).
  • To confirm the theoretical basis for transient chaos in these systems.

Main Methods:

  • Analysis of the system's underlying structure.
  • Identification and construction of fixed points and their pre-images.

Related Experiment Videos

  • Parameter allocation to induce specific dynamical behaviors.

    • Main Results:

    • Existence of snap-back repellers confirmed, leading to transversal homoclinic orbits.
    • Chaotic dynamics, as defined by Li-Yorke or Marotto, are demonstrated.
    • Theoretical confirmation of transient chaos scenarios within the network.

    Conclusions:

    • The study provides a theoretical framework for transient chaos in discrete-time neural networks.
    • Numerical examination of parameter conditions offers insights into chaotic and convergent dynamics.
    • Findings are significant for applying transiently chaotic neural networks to combinatorial optimization problems, particularly in annealing processes.