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Assembly and Characterization of an External Driver for the Generation of Sub-Kilohertz Oscillatory Flow in Microchannels
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Between phase and amplitude oscillators.

Pau Clusella1,2, Antonio Politi1

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This study introduces a new model for amplitude oscillators, revealing a transition to self-consistent partial synchrony (SCPS) and a novel form of collective chaos. The findings enhance understanding of macroscopic and microscopic dynamics in oscillator systems.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Amplitude oscillators often exhibit collective behaviors, but intermediate regimes remain less understood.
  • Existing models typically focus on phase oscillators, limiting analysis of amplitude dynamics.
  • The relationship between macroscopic and microscopic descriptions in oscillator networks requires further investigation.

Purpose of the Study:

  • To analyze an intermediate collective regime of amplitude oscillators.
  • To develop a general formalism for describing oscillator dynamics and curve evolution.
  • To identify and characterize novel collective behaviors like self-consistent partial synchrony and collective chaos.

Main Methods:

  • Development of a general formalism using two partial differential equations.
  • Analysis of probability density evolution along a time-dependent curve C.
  • Application to Stuart-Landau oscillators and generalization to other amplitude oscillators.

Main Results:

  • Identification and characterization of a transition to self-consistent partial synchrony (SCPS).
  • Analytical treatment and stability analysis of SCPS, highlighting the role of higher Fourier harmonics.
  • Discovery of a generalized collective chaos with a multifractal probability density.

Conclusions:

  • The developed formalism effectively describes macroscopic and microscopic dynamics of amplitude oscillators.
  • The study elucidates the critical role of higher Fourier harmonics in coupling functions.
  • New insights into collective behaviors, including SCPS and collective chaos, are provided.