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Title: Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

Abstract

Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.

Authors:
 [1]; ORCiD logo [1];  [2];  [3];  [3]
  1. Univ. of Massachusetts, Amherst, MA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
  3. Univ. of Pittsburgh, PA (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1257982
Alternate Identifier(s):
OSTI ID: 1359741
Report Number(s):
LA-UR-15-23080
Journal ID: ISSN 0167-2789; PII: S0167278916000178
Grant/Contract Number:
FA9550-12-1-0332; FP7; IRSES-605096; DMS-1312508; AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Volume: 325; Journal Issue: C; Journal ID: ISSN 0167-2789
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES; 97 MATHEMATICS AND COMPUTING; Coupled nonlinear oscillators; Discrete model; Traveling waves

Citation Formats

Duanmu, M., Whitaker, N., Kevrekidis, P. G., Vainchtein, A., and Rubin, J. E.. Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators. United States: N. p., 2016. Web. doi:10.1016/j.physd.2016.02.001.
Duanmu, M., Whitaker, N., Kevrekidis, P. G., Vainchtein, A., & Rubin, J. E.. Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators. United States. doi:10.1016/j.physd.2016.02.001.
Duanmu, M., Whitaker, N., Kevrekidis, P. G., Vainchtein, A., and Rubin, J. E.. Sat . "Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators". United States. doi:10.1016/j.physd.2016.02.001. https://www.osti.gov/servlets/purl/1257982.
@article{osti_1257982,
title = {Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators},
author = {Duanmu, M. and Whitaker, N. and Kevrekidis, P. G. and Vainchtein, A. and Rubin, J. E.},
abstractNote = {Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.},
doi = {10.1016/j.physd.2016.02.001},
journal = {Physica. D, Nonlinear Phenomena},
number = C,
volume = 325,
place = {United States},
year = {Sat Feb 27 00:00:00 EST 2016},
month = {Sat Feb 27 00:00:00 EST 2016}
}

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Cited by: 3 works
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