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Sinusoidal and nonsinusoidal patterns in amplitude envelope synchronization.

Hanchang Liu1, Weiqing Liu1, Chaoxin Fu2

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Summary
This summary is machine-generated.

Amplitude envelope synchronization (AES) in coupled nonlinear systems shows two patterns: sinusoidal and nonsinusoidal. Frequency mismatch influences the pattern, revealing general dynamics in coupled oscillators.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Synchronization Phenomena

Background:

  • Coupled nonlinear systems exhibit complex dynamics.
  • Synchronization is a key phenomenon in various scientific fields.
  • Amplitude envelope synchronization (AES) involves correlated amplitude but uncorrelated phase/frequency.

Purpose of the Study:

  • Investigate amplitude envelope synchronization (AES) in coupled nonidentical nonlinear systems.
  • Characterize different patterns of AES.
  • Reveal the underlying physical mechanisms and scale relations of AES.

Main Methods:

  • Theoretical analysis of coupled nonlinear oscillators.
  • Numerical simulations to observe AES patterns.
  • Synchronization manifold and transverse stability analyses.

Main Results:

  • Identified two distinct AES patterns: sinusoidal and nonsinusoidal.
  • Demonstrated that frequency mismatch drives the crossover from nonsinusoidal to sinusoidal AES.
  • Revealed the physical mechanisms and scale relations governing AES.

Conclusions:

  • AES is a general phenomenon in coupled nonlinear oscillators.
  • Understanding AES dynamics is crucial for multidisciplinary fields involving coupled systems.
  • Results provide insights into phase and amplitude coupling in complex systems.