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Title: Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators

Abstract

Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description ofmore » the high-dimensional attractor-basin architecture.« less

Authors:
 [1];  [2]; ;  [3];  [1];  [2];  [1];  [2];  [2];  [2];  [1];  [2];  [2];  [2]
  1. Complexity Sciences Center, University of California, Davis, California 95616 (United States)
  2. (United States)
  3. William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States)
Publication Date:
OSTI Identifier:
22596561
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 9; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; LIMIT CYCLE; NONLINEAR PROBLEMS; OSCILLATORS; STOCHASTIC PROCESSES; SYNCHRONIZATION; TOPOLOGY; TRAJECTORIES

Citation Formats

Emenheiser, Jeffrey, Department of Physics, University of California, Davis, California 95616, Chapman, Airlie, Mesbahi, Mehran, Pósfai, Márton, Department of Computer Science, University of California, Davis, California 95616, Crutchfield, James P., Department of Physics, University of California, Davis, California 95616, Department of Computer Science, University of California, Davis, California 95616, Santa Fe Institute, Santa Fe, New Mexico 87501, D'Souza, Raissa M., Department of Computer Science, University of California, Davis, California 95616, Santa Fe Institute, Santa Fe, New Mexico 87501, and Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616. Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators. United States: N. p., 2016. Web. doi:10.1063/1.4960191.
Emenheiser, Jeffrey, Department of Physics, University of California, Davis, California 95616, Chapman, Airlie, Mesbahi, Mehran, Pósfai, Márton, Department of Computer Science, University of California, Davis, California 95616, Crutchfield, James P., Department of Physics, University of California, Davis, California 95616, Department of Computer Science, University of California, Davis, California 95616, Santa Fe Institute, Santa Fe, New Mexico 87501, D'Souza, Raissa M., Department of Computer Science, University of California, Davis, California 95616, Santa Fe Institute, Santa Fe, New Mexico 87501, & Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616. Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators. United States. doi:10.1063/1.4960191.
Emenheiser, Jeffrey, Department of Physics, University of California, Davis, California 95616, Chapman, Airlie, Mesbahi, Mehran, Pósfai, Márton, Department of Computer Science, University of California, Davis, California 95616, Crutchfield, James P., Department of Physics, University of California, Davis, California 95616, Department of Computer Science, University of California, Davis, California 95616, Santa Fe Institute, Santa Fe, New Mexico 87501, D'Souza, Raissa M., Department of Computer Science, University of California, Davis, California 95616, Santa Fe Institute, Santa Fe, New Mexico 87501, and Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616. 2016. "Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators". United States. doi:10.1063/1.4960191.
@article{osti_22596561,
title = {Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators},
author = {Emenheiser, Jeffrey and Department of Physics, University of California, Davis, California 95616 and Chapman, Airlie and Mesbahi, Mehran and Pósfai, Márton and Department of Computer Science, University of California, Davis, California 95616 and Crutchfield, James P. and Department of Physics, University of California, Davis, California 95616 and Department of Computer Science, University of California, Davis, California 95616 and Santa Fe Institute, Santa Fe, New Mexico 87501 and D'Souza, Raissa M. and Department of Computer Science, University of California, Davis, California 95616 and Santa Fe Institute, Santa Fe, New Mexico 87501 and Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616},
abstractNote = {Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.},
doi = {10.1063/1.4960191},
journal = {Chaos (Woodbury, N. Y.)},
number = 9,
volume = 26,
place = {United States},
year = 2016,
month = 9
}
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