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

Multivalued mappings in generalized chaos synchronization.

N F Rulkov1, V S Afraimovich, C T Lewis

  • 1Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 20, 2001
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

Emergency intubation in trauma in KwaZulu-Natal Province, South Africa.

South African medical journal = Suid-Afrikaanse tydskrif vir geneeskunde·2018
Same author

Mind-to-mind heteroclinic coordination: Model of sequential episodic memory initiation.

Chaos (Woodbury, N.Y.)·2018
Same author

Sexual behaviour of backpackers who visit Koh Tao and Koh Phangan, Thailand: a cross-sectional study.

Sexually transmitted infections·2016
Same author

One fungus, which genes? Development and assessment of universal primers for potential secondary fungal DNA barcodes.

Persoonia·2016
Same author

Timing control by redundant inhibitory neuronal circuits.

Chaos (Woodbury, N.Y.)·2014
Same author

Relating the sequential dynamics of excitatory neural networks to synaptic cellular automata.

Chaos (Woodbury, N.Y.)·2012
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 explores generalized synchronization of chaos in coupled systems, extending theory to multivalued mappings. We investigate synchronization with non-one-to-one frequency ratios, analyzing mapping properties and continuity.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Generalized synchronization of chaos involves a continuous mapping between drive and response systems.
  • Existing theories primarily address single-valued synchronization mappings.
  • Understanding multivalued mappings is crucial for broader applications.

Purpose of the Study:

  • To investigate generalized synchronization in systems exhibiting multivalued synchronization mappings.
  • To analyze the properties of these multivalued mappings, including their existence and continuity.
  • To develop a theoretical framework for synchronization regimes with non-one-to-one frequency ratios.

Main Methods:

  • Analysis of dynamical systems with directional coupling.
  • Characterization of the synchronization mapping between drive and response systems.

Related Experiment Videos

  • Theoretical development for multivalued mapping scenarios.

    • Main Results:

    • Demonstration of generalized synchronization with multivalued mappings.
    • Identification of conditions for the existence and continuity of these mappings.
    • Characterization of synchronization under non-one-to-one frequency ratios.

    Conclusions:

    • Generalized synchronization can occur with multivalued mappings.
    • The study extends the theory of chaos synchronization to more complex regimes.
    • The developed framework supports understanding coupled chaotic systems with diverse frequency relationships.