Mechanisms for Producing Oscillatory Plane Waves in Discrete and Continuum Models

SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page S151-S171, June 2024.
Abstract. Plane waves have commonly been observed in recordings of human brains. These waves take the form of spatial phase gradients in the oscillatory potentials picked up by implanted electrodes. We first show that long but finite chains of nearest-neighbor coupled phase oscillators can produce an almost constant phase gradient when the edge effects interact with small heterogeneities in the local frequency. Next, we introduce a continuum model with nonlocal coupling and use singular perturbation methods to show similar interactions between the boundaries and small frequency differences. Finally, we show that networks of Wilson–Cowan equations can generate plane waves with the same mechanism.



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