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Rafael M da Silva1, Cesar Manchein2, Marcus W Beims1,3

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Summary
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This study investigates intermittent stickiness synchronization (ISS) in Hamiltonian systems using finite-time Lyapunov exponents (FTLEs). We found universal behavior in time correlation decay, with full synchronization being rare but long-lasting due to slow decay.

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Area of Science:

  • * Nonlinear Dynamics
  • * Statistical Physics
  • * Hamiltonian Systems

Background:

  • * Stickiness Synchronization (SS) describes chaotic trajectories approaching regular structures in phase space.
  • * Full SS occurs when all finite-time Lyapunov exponents (FTLEs) approach zero, indicating collective motion.
  • * Partial SS involves at least one FTLE approaching zero, with varying degrees based on system parameters.

Purpose of the Study:

  • * To investigate intermittent stickiness synchronization (ISS) in high-dimensional Hamiltonian systems.
  • * To analyze the statistical properties of FTLEs and their relation to synchronization phenomena.
  • * To characterize the algebraic decay exponents of ISS and explore universal behaviors in time correlation decay.

Main Methods:

  • * Statistical analysis of finite-time Lyapunov exponents (FTLEs).
  • * Application of filtering procedures to characterize sticky motion.
  • * Computation of algebraic decay exponents for intermittent stickiness synchronization.

Main Results:

  • * Evidence of universal behavior in the decay of time correlations, linked to algebraic decay exponents.
  • * Identification of distinct degrees of partial SS influenced by system parameters and dimensionality.
  • * Demonstration that full SS, though improbable, can persist for extended periods due to slow correlation decay.

Conclusions:

  • * The study reveals universal properties in time correlation decay within mixed phase spaces of Hamiltonian systems.
  • * Intermittent stickiness synchronization exhibits slow algebraic decay, leading to rare but prolonged full synchronization events.
  • * Findings contribute to understanding chaotic dynamics and synchronization phenomena in complex systems.