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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
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Chimera states as chaotic spatiotemporal patterns.

Oleh E Omel'chenko1, Matthias Wolfrum, Yuri L Maistrenko

  • 1Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Chimera states exhibit irregular, Brownian-like motion in their coherent and incoherent regions. This finite-size effect, observed in nonlocally coupled oscillators, is not seen in the thermodynamic limit.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Statistical physics

Background:

  • Chimera states are a recently discovered dynamical phenomenon in nonlocally coupled oscillator arrays.
  • They exhibit a unique spatial pattern characterized by coexisting coherent and incoherent regions.

Purpose of the Study:

  • To report an additional feature of chimera states: the irregular motion of their spatial patterns.
  • To characterize this motion as a spatiotemporal pattern with regular spatial structure and irregular temporal dynamics.
  • To investigate this motion as a finite-size effect and its dependence on system parameters.

Main Methods:

  • Numerical simulations of nonlocally coupled oscillator arrays.
  • Analysis of spatial patterns and their temporal evolution.
  • Statistical analysis to describe the motion on large time scales.

Main Results:

  • Chimera states exhibit irregular motion of their coherent and incoherent regions.
  • This motion is a finite-size effect, absent in the thermodynamic limit.
  • On large timescales, the motion can be described as Brownian motion.
  • The motion's dependence on the number of oscillators (N) and system parameters was studied.

Conclusions:

  • Chimera states possess a dynamic component characterized by irregular spatiotemporal motion.
  • This irregular motion is a crucial characteristic of finite-sized chimera systems.
  • The Brownian motion description provides a framework for understanding the temporal dynamics of chimera states.