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

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.

doi:10.1016/j.physd.2016.02.001

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

Journal Article · Sat Feb 27 00:00:00 EST 2016 · Physica. D, Nonlinear Phenomena

DOI:https://doi.org/10.1016/j.physd.2016.02.001· OSTI ID:1257982

Duanmu, M. ^[1];

^[1]; Kevrekidis, P. G. ^[2]; Vainchtein, A. ^[3]; Rubin, J. E. ^[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)

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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FA9550-12-1-0332; FP7; IRSES-605096; DMS-1312508; AC52-06NA25396

OSTI ID:: 1257982

Alternate ID(s):: OSTI ID: 1359741

Report Number(s):: LA-UR-15-23080; PII: S0167278916000178

Journal Information:: Physica. D, Nonlinear Phenomena, Vol. 325, Issue C; ISSN 0167-2789

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 10 works

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References (24)

Cellular mechanisms underlying the pharmacological induction of phosphenes: Mechanisms underlying phosphene induction Cervetto, L.; Demontis, G. C.; Gargini, C. British Journal of Pharmacology, Vol. 150, Issue 4 https://doi.org/10.1038/sj.bjp.0706998	journal	February 2007
Will Retinal Implants Restore Vision? Zrenner, E. Science, Vol. 295, Issue 5557 https://doi.org/10.1126/science.1067996	journal	February 2002
Electrical induction of vision Tehovnik, Edward J.; Slocum, Warren M. Neuroscience & Biobehavioral Reviews, Vol. 37, Issue 5 https://doi.org/10.1016/j.neubiorev.2013.03.012	journal	June 2013
Contour-like phosphenes from electrical stimulation of the human eye: some new observations Carpenter, R. H. S. The Journal of Physiology, Vol. 229, Issue 3 https://doi.org/10.1113/jphysiol.1973.sp010166	journal	March 1973
Phase Boundaries as Electrically Induced Phosphenes Drover, Jonathan D.; Ermentrout, G. Bard SIAM Journal on Applied Dynamical Systems, Vol. 5, Issue 4 https://doi.org/10.1137/050646469	journal	January 2006
The dynamics of a forced coupled network of active elements Parks, Helen F.; Ermentrout, Bard; Rubin, Jonathan E. Physica D: Nonlinear Phenomena, Vol. 240, Issue 7 https://doi.org/10.1016/j.physd.2010.11.006	journal	March 2011
Wave Front Depinning Transition in Discrete One-Dimensional Reaction-Diffusion Systems Carpio, A.; Bonilla, L. Physical Review Letters, Vol. 86, Issue 26 https://doi.org/10.1103/PhysRevLett.86.6034	journal	June 2001
Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit Friesecke, G.; Pego, R. L. Nonlinearity, Vol. 12, Issue 6 https://doi.org/10.1088/0951-7715/12/6/311	journal	October 1999
Solitary waves on FPU lattices: II. Linear implies nonlinear stability Friesecke, G.; Pego, R. L. Nonlinearity, Vol. 15, Issue 4 https://doi.org/10.1088/0951-7715/15/4/317	journal	June 2002
Solitary waves on Fermi–Pasta–Ulam lattices: III. Howland-type Floquet theory Friesecke, G.; Pego, R. L. Nonlinearity, Vol. 17, Issue 1 https://doi.org/10.1088/0951-7715/17/1/013	journal	October 2003
Solitary waves on Fermi–Pasta–Ulam lattices: IV. Proof of stability at low energy Friesecke, G.; Pego, R. L. Nonlinearity, Vol. 17, Issue 1 https://doi.org/10.1088/0951-7715/17/1/014	journal	October 2003
On the solitary wave pulse in a chain of beads English, J. M.; Pego, R. L. Proceedings of the American Mathematical Society, Vol. 133, Issue 6, p. 1763-1768 https://doi.org/10.1090/S0002-9939-05-07851-2	journal	January 2005
Traveling waves for monomer chains with precompression Stefanov, Atanas; Kevrekidis, Panayotis Nonlinearity, Vol. 26, Issue 2 https://doi.org/10.1088/0951-7715/26/2/539	journal	January 2013
Bifurcations of travelling wave solutions in the discrete NLS equations Pelinovsky, Dmitry E.; Rothos, Vassilis M. Physica D: Nonlinear Phenomena, Vol. 202, Issue 1-2 https://doi.org/10.1016/j.physd.2005.01.016	journal	March 2005
Translationally invariant nonlinear Schrödinger lattices Pelinovsky, Dmitry E. Nonlinearity, Vol. 19, Issue 11 https://doi.org/10.1088/0951-7715/19/11/010	journal	October 2006
Moving solitons in the discrete nonlinear Schrödinger equation Oxtoby, O. F.; Barashenkov, I. V. Physical Review E, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevE.76.036603	journal	September 2007
Radiationless Traveling Waves in Saturable Nonlinear Schrödinger Lattices Melvin, T. R. O.; Champneys, A. R.; Kevrekidis, P. G. Physical Review Letters, Vol. 97, Issue 12 https://doi.org/10.1103/PhysRevLett.97.124101	journal	September 2006
Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity: Existence, stability and dynamics Melvin, T. R. O.; Champneys, A. R.; Kevrekidis, P. G. Physica D: Nonlinear Phenomena, Vol. 237, Issue 4 https://doi.org/10.1016/j.physd.2007.09.026	journal	April 2008
Variational approximations for traveling solitons in a discrete nonlinear Schrödinger equation Syafwan, M.; Susanto, H.; Cox, S. M. Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 7 https://doi.org/10.1088/1751-8113/45/7/075207	journal	February 2012
Stimulus-Locked Traveling Waves and Breathers in an Excitatory Neural Network Folias, Stefanos E.; Bressloff, Paul C. SIAM Journal on Applied Mathematics, Vol. 65, Issue 6 https://doi.org/10.1137/040615171	journal	January 2005
Stimulus-Driven Traveling Solutions in Continuum Neuronal Models with a General Smooth Firing Rate Function Ermentrout, G. Bard; Jalics, Jozsi Z.; Rubin, Jonathan E. SIAM Journal on Applied Mathematics, Vol. 70, Issue 8 https://doi.org/10.1137/090775737	journal	January 2010
A Coupled Base-Rotator Model for Structure and Dynamics of DNA: Local Fluctuations in Helical Twist Angles and Topological Solitons Homma, S.; Takeno, S. Progress of Theoretical Physics, Vol. 72, Issue 4 https://doi.org/10.1143/PTP.72.679	journal	October 1984
Kinks and Breathers Associated with Collective Sugar Puckering in DNA Takeno, S.; Homma, S. Progress of Theoretical Physics, Vol. 77, Issue 3 https://doi.org/10.1143/PTP.77.548	journal	March 1987
Kink shape modes and resonant dynamics in sine-lattices Zhang, Fei Physica D: Nonlinear Phenomena, Vol. 110, Issue 1-2 https://doi.org/10.1016/S0167-2789(97)00113-9	journal	December 1997

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