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Article
Dynamics of Locally Coupled Oscillators with Next-Nearest-Neighbor Interaction
Journal of Physics A: Mathematical and Theoretical
  • J. Herbrych, University of Crete
  • A. G. Chazirakis, University of Crete
  • N. Christakis, University of Crete
  • J. J. P. Veerman, Portland State University
Document Type
Pre-Print
Publication Date
6-1-2015
Subjects
  • Dynamical Systems,
  • Optimization and operations research,
  • Multiagent Systems
Disciplines
Abstract
A theoretical description of decentralized dynamics within linearly coupled, one-dimensional oscillators (agents) with up to next-nearest-neighbor interaction is given. Conditions for stability of such system are presented. Our results indicate that the stable systems have response that grow at least linearly in the system size. We give criteria when this is the case. The dynamics of these systems can be described with traveling waves with strong damping in the high frequencies. Depending on the system parameters, two types of solutions have been found: damped oscillations and reflectionless waves. The latter is a novel result and a feature of systems with at least next-nearest-neighbor interactions. Analytical predictions are tested in numerical simulations.
Description

This is the pre-print version of an article submitted for consideration in the Journal of Physics A: Mathematical and Theoretical. Copyright (2015) IOP Publishing

Persistent Identifier
http://archives.pdx.edu/ds/psu/17422
Citation Information
Herbrych, J., Chazirakis, A. G., Christakis, N., & Veerman, J. J. P. (2015). Dynamics of locally coupled oscillators with next-nearest-neighbor interaction. arXiv preprint arXiv:1506.07381.