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Occasional uncoupling overcomes measure desynchronization.

Anupam Ghosh1, Tirth Shah2, Sagar Chakraborty1

  • 1Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India.

Chaos (Woodbury, N.Y.)
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Measure synchronization in Hamiltonian systems is explored. Occasional uncoupling can restore measure synchrony in desynchronized states, with analytical results for periodic uncoupling strategies.

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Area of Science:

  • * Hamiltonian dynamics
  • * Nonlinear systems theory
  • * Synchronization phenomena

Background:

  • * Identical synchronization is inapplicable to Hamiltonian systems due to the absence of phase space attractors.
  • * Measure synchronization is a generalized phenomenon defined for Hamiltonian systems.
  • * Coupled Hamiltonian systems can exhibit quasiperiodic or chaotic measure synchronized states.

Purpose of the Study:

  • * To investigate measure synchronization in coupled Hamiltonian systems.
  • * To identify conditions leading to measure desynchronization.
  • * To explore methods for restoring measure synchrony.

Main Methods:

  • * Analysis of representative quasiperiodic and chaotic coupled Hamiltonian systems.
  • * Variation of coupling strengths to study parameter intervals of desynchronization.
  • * Investigation of occasional and periodic uncoupling strategies to restore synchrony.

Main Results:

  • * Intervals of coupling parameters exist where measure desynchronization occurs.
  • * Temporarily switching off coupling can re-establish measure synchrony from a desynchronized state.
  • * Analytical solutions are derived for the on-fraction of periodic uncoupling required for synchrony.

Conclusions:

  • * Measure desynchronization is a possible state in coupled Hamiltonian systems.
  • * Occasional uncoupling is an effective strategy to recover measure synchrony.
  • * The study provides analytical insights into optimizing periodic uncoupling for synchronization.