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

Countable and uncountable boundaries in chaotic scattering.

Alessandro P S De Moura1, Celso Grebogi

  • 1Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
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

Chaotic ghosts in systems with parameter drift: Delay and control critical transitions.

Physical review. E·2026
Same author

Multiscale spatiotemporal neural network with multi-attention mechanism using brain partitioning for motor imagery recognition.

Journal of neuroscience methods·2026
Same author

Complex bifurcation structures in a Hodgkin-Huxley model of thermally sensitive neurons under periodic perturbation.

Physical review. E·2025
Same author

Adaptive Whole-Brain Dynamics Predictive Method: Relevancy to Mental Disorders.

Research (Washington, D.C.)·2025
Same author

Unsupervised Domain Adaptation With Synchronized Self-Training for Cross- Domain Motor Imagery Recognition.

IEEE journal of biomedical and health informatics·2025
Same author

Transcriptomic Evidence Reveals the Dysfunctional Mechanism of Synaptic Plasticity Control in ASD.

Genes·2025
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

This study classifies basin boundaries in open chaotic Hamiltonian systems into Type I (Cantor sets) and Type II (Cantor sets with isolated points). Boundary type depends on system topology and escape definitions, with a potential energy-driven transition.

Area of Science:

  • Complex Systems
  • Dynamical Systems Theory
  • Statistical Mechanics

Background:

  • Open chaotic Hamiltonian systems exhibit complex dynamics.
  • Understanding basin boundaries is crucial for predicting system behavior and stability.

Purpose of the Study:

  • To topologically classify basin boundaries in open chaotic Hamiltonian systems.
  • To identify factors determining boundary type and potential transitions.

Main Methods:

  • Topological analysis of basin boundaries.
  • Intersection analysis with one-dimensional curves.
  • Investigation of configuration space topology and escape definitions.

Main Results:

  • Basin boundaries are classified as Type I (Cantor set) or Type II (Cantor set plus isolated points).

Related Experiment Videos

  • Boundary type is determined by configuration space topology and escape definitions.
  • A transition from Type I to Type II boundaries can occur at a critical energy value.

    • Conclusions:

    • The topological classification provides a framework for understanding basin boundary complexity.
    • System energy and escape definitions significantly influence boundary structure.
    • The findings are illustrated using a two-dimensional scattering system example.