We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from other oscillators in its neighborhood. Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)] and adopting a strategy similar to that employed in the recent work of Laing [Physica D 238, 1569 (2009)], we reduce the microscopic dynamics of these systems to a macroscopic partial-differential-equation description. Using this macroscopic formulation, we numerically find that finite oscillator response time leads to interesting spatiotemporal dynamical behaviors including propagating fronts, spots, target patterns, chimerae, spiral waves, etc., and we study interactions and evolutionary behaviors of these spatiotemporal patterns.
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June 2011
Research Article|
June 24 2011
Dynamics and pattern formation in large systems of spatially-coupled oscillators with finite response times
Wai Shing Lee;
Wai Shing Lee
1Institute for Research in Electronics and Applied Physics,
University of Maryland
, College Park, Maryland 20742, USA
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Juan G. Restrepo;
Juan G. Restrepo
2Department of Applied Mathematics,
University of Colorado
, Boulder, Colorado 80309, USA
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Edward Ott;
Edward Ott
1Institute for Research in Electronics and Applied Physics,
University of Maryland
, College Park, Maryland 20742, USA
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Thomas M. Antonsen
Thomas M. Antonsen
1Institute for Research in Electronics and Applied Physics,
University of Maryland
, College Park, Maryland 20742, USA
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Chaos 21, 023122 (2011)
Article history
Received:
January 03 2011
Accepted:
May 08 2011
Citation
Wai Shing Lee, Juan G. Restrepo, Edward Ott, Thomas M. Antonsen; Dynamics and pattern formation in large systems of spatially-coupled oscillators with finite response times. Chaos 1 June 2011; 21 (2): 023122. https://doi.org/10.1063/1.3596697
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