Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators
Abstract
Following the longlived qualitativedynamics 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 amplitudephase oscillators arranged in a ring topology with reactive nearestneighbor 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 noiseinduced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractorswitching 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 coarsegrained description ofmore »
 Authors:
 Complexity Sciences Center, University of California, Davis, California 95616 (United States)
 (United States)
 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 longlived qualitativedynamics 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 amplitudephase oscillators arranged in a ring topology with reactive nearestneighbor 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 noiseinduced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractorswitching 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 coarsegrained description of the highdimensional attractorbasin 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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