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

Targeting unknown and unstable periodic orbits.

B Doyon1, L J Dubé

  • 1Département de Physique, de Génie Physique, et d'Optique, Université Laval, Cité Universitaire, Québec, Canada G1K 7P4.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 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

Generalized Hydrodynamics on an Atom Chip.

Physical review letters·2019
Same author

Light-induced chaotic rotations in nematic liquid crystals.

Physical review. E, Statistical, nonlinear, and soft matter physics·2006
Same author

On Jacobian matrices for flows.

Chaos (Woodbury, N.Y.)·2005
Same author

Optically induced dynamics in nematic liquid crystals: The role of finite beam size.

Physical review. E, Statistical, nonlinear, and soft matter physics·2004
Same author

Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry.

Physical review. E, Statistical, nonlinear, and soft matter physics·2003
Same author

Automatic grapheme processing in the left occipitotemporal cortex.

Neuroreport·2002
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 introduces a novel targeting method to control unstable periodic orbits in complex dynamical systems. The technique enables navigation between chaotic and stable regions, applicable to various systems.

Area of Science:

  • Dynamical Systems Theory
  • Chaos Theory
  • Nonlinear Dynamics

Background:

  • Complex systems often exhibit mixed dynamics, with coexisting regular and chaotic regions.
  • Controlling specific orbits within these mixed systems is challenging due to unknown stability and position.

Purpose of the Study:

  • To present a general method for targeting and controlling orbits of specified period.
  • To enable navigation from chaotic to stable regions and vice versa within complex dynamical systems.

Main Methods:

  • Development of a targeting algorithm for dynamical systems.
  • Application to systems with mixed regular and chaotic dynamics.
  • Demonstration of control on unstable periodic orbits.

Main Results:

Related Experiment Videos

  • The method successfully targets orbits with specified periods, regardless of their initial stability or position.
  • It allows for controlled transitions from chaotic to unstable periodic orbits.
  • The technique facilitates access to stable phase space regions from stochastic domains.

Conclusions:

  • The presented targeting algorithm is a versatile tool for controlling orbits in complex dynamical systems.
  • It offers a pathway to manage system dynamics across chaotic and regular regions.
  • The method's generality extends to both conservative and dissipative systems, including discrete maps and continuous flows.