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Steady and Traveling Wave Solutions in a Chain of Periodically Forced Couple Nonlinear Oscillators

Banff International Research Station for Mathematical Innovation and Discovery

Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze trav- eling 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 system- atically 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 and annihilation of radial ones. Finally, we show that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.

Mathematics; Partial differential equations; Dynamical systems and ergodic theory

video/mp4

Author affiliation: University of Massachusetts

2017-01-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60066

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/