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

• Stimulated retina cells associated with phosphene induction are modeled by a chain of coupled nonlinear oscillators.
• Traveling wave solutions, which exist in a certain parameter regime, are obtained.
• Stability regions for the obtained solutions are identified in parameter space.
• A two-dimensional extension of the model is considered.
• Two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations.

Motivated by earlier studies of artificial perceptions of light called phosphenes, 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. 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.