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Related Experiment Videos

Mechanism for the partial synchronization in three coupled chaotic systems.

Woochang Lim1, Sang-Yoon Kim

  • 1Department of Physics, Kangwon National University, Chunchon, Kangwon-Do 200-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary

Partial synchronization in coupled systems arises from blowout bifurcations. The stability of intermittent states, determined by laminar versus bursting components, dictates whether partial synchronization or complete desynchronization occurs.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Coupled dynamical systems can exhibit various synchronization patterns.
  • Blowout bifurcations are a key mechanism for the loss of complete synchronization.
  • Partial synchronization involves clusters of synchronized elements within a larger system.

Purpose of the Study:

  • To elucidate the dynamical mechanism behind partial synchronization in three coupled one-dimensional maps.
  • To investigate the role of blowout bifurcations and intermittent states in achieving partial synchronization.
  • To determine the factors influencing the transition between partial synchronization and complete desynchronization.

Main Methods:

  • Analysis of attractor stability in coupled map lattices.

Related Experiment Videos

  • Identification of blowout bifurcations and their impact on system dynamics.
  • Characterization of intermittent two-cluster states and their transverse stability.
  • Examination of the competition between laminar and bursting components of intermittent states.

    • Main Results:

    • Complete synchronization is lost via blowout bifurcations, leading to two-cluster states with on-off intermittency.
    • Partial synchronization occurs if the intermittent two-cluster state is transversely stable.
    • The dominance of laminar or bursting components determines the system's final state (partial synchronization or desynchronization).
    • This mechanism was validated in coupled multidimensional systems like He non maps and pendula.

    Conclusions:

    • Partial synchronization in coupled systems is driven by blowout bifurcations and the properties of emergent intermittent states.
    • The balance between laminar and bursting dynamics within intermittent states is crucial for determining synchronization outcomes.
    • The findings offer a unified mechanism for partial synchronization across different coupled nonlinear systems.