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Chimera states for coupled oscillators.

Daniel M Abrams1, Steven H Strogatz

  • 1Department of Theoretical and Applied Mechanics, Cornell University, 212 Kimball Hall, Ithaca, New York 14853-1503, USA. dma32@cornell.edu

Physical Review Letters
|November 5, 2004
PubMed
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Researchers found an exact solution for chimera states in nonlocally coupled oscillator arrays. This complex spatiotemporal pattern, where locked and drifting oscillators coexist, is now mathematically described.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Theoretical Physics

Background:

  • Chimera states, a coexistence of phase-locked and drifting identical oscillators, were recently discovered.
  • These states were thought to be exclusive to nonlocally coupled systems, not local or global ones.

Purpose of the Study:

  • To provide an exact mathematical solution for chimera states.
  • To analyze the stability and bifurcation of chimera states in a specific system.

Main Methods:

  • Developed an exact analytical solution for a ring of phase oscillators.
  • Utilized a cosine coupling kernel for nonlocal interactions.
  • Analyzed bifurcations from a spatially modulated drift state.

Main Results:

Related Experiment Videos

  • Presented an exact solution for chimera states in a ring of nonlocally coupled phase oscillators.
  • Demonstrated that the stable chimera state emerges from a spatially modulated drift state.
  • Showed the chimera state terminates via a saddle-node bifurcation with an unstable chimera state.

Conclusions:

  • The study provides a fundamental analytical description of chimera states.
  • This work clarifies the dynamics and stability of chimera states in nonlocally coupled systems.
  • Offers a basis for further theoretical and experimental investigations of complex oscillator dynamics.