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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. [ABSTRACT FROM AUTHOR]

Rotating waves are a common occurrence in large scale recordings of brain oscillations. We examine the existence, stability, and form of rigid rotating waves in a nonlocally coupled phase model on the annulus. For odd interaction functions, it is possible to write down an explicit solution. When interactions are more general, we prove existence of the waves and use perturbation theory to estimate the shape, frequency, and stability of the waves. For large holes, we show that the phase satisfies a Burgers-type equation. We show that as the hole in the annulus decreases, the waves lose stability. Through numerical simulations, we suggest that the bifurcation that occurs with the shrinking hole is a saddle-node infinite cycle and gives rise to so-called spiral chimeras. [ABSTRACT FROM AUTHOR]

Two simple algorithms based on combining odor concentration differences across time and space along with information on the flow direction are tested for their ability to locate an odor source in four different odor landscapes. Image data taken from air plumes in three different regimes and a water plume are used as test environments for a bilateral ("stereo sampling") algorithm using concentration differences across two sensors and a "casting" algorithm that uses successive samples to decide orientation. Agents are started at random locations and orientations in the landscape and allowed to move until they reach the source of the odor (success) or leave the imaged area (failure). Parameters for the algorithm are chosen to optimize success and to minimize path length to the source. Success rates over 90% are consistently obtained with path lengths that can be as low as twice the starting distance from the source in air and four times the distance in the highly turbulent water plumes. We find that parameters that optimize success often lead to more exploratory pathways to the source. Information about the direction from which the odor is coming is necessary for successful navigation in the water plume and reduces the path length in the three tested air plumes., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)