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

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;
^{[2]};
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^{[3]}
 Univ. of Massachusetts, Amherst, MA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
 Univ. of Pittsburgh, PA (United States)
 Publication Date:
 Report Number(s):
 LAUR1523080
Journal ID: ISSN 01672789; PII: S0167278916000178
 Grant/Contract Number:
 FA95501210332; FP7; IRSES605096; DMS1312508; AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Physica. D, Nonlinear Phenomena
 Additional Journal Information:
 Journal Volume: 325; Journal Issue: C; Journal ID: ISSN 01672789
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 59 BASIC BIOLOGICAL SCIENCES; 97 MATHEMATICS AND COMPUTING; Coupled nonlinear oscillators; Discrete model; Traveling waves
 OSTI Identifier:
 1257982
 Alternate Identifier(s):
 OSTI ID: 1359741
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.,
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.. 2016.
"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 cotraveling 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 twodimensional 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 = {2016},
month = {2}
}