Mechanisms for producing oscillatory plane waves in discrete and continuum models

DOI10.1137/22m1506523MaRDI QIDQ6597816

Andrea J. Welsh, Bard Ermentrout

Publication date: 4 September 2024

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

coupled oscillatorsintegral equationscortical waves

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Neural biology (92C20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Singular perturbations for ordinary differential equations (34E15)

Cites Work

• Mathematical foundations of neuroscience
• Coupled oscillators and the design of central pattern generators
• The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model
• Waves, bumps, and patterns in neural field theories
• Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses
• Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
• Phase Transitions and Other Phenomena in Chains of Coupled Oscillators
• Symmetry and phaselocking in chains of weakly coupled oscillators
• Stable Periodic Solutions to Discrete and Continuum Arrays of Weakly Coupled Nonlinear Oscillators
• Monotonicity of Phaselocked Solutions in Chains and Arrays of Nearest-Neighbor Coupled Oscillators
• Stimulus-Driven Traveling Solutions in Continuum Neuronal Models with a General Smooth Firing Rate Function

This page was built for publication: Mechanisms for producing oscillatory plane waves in discrete and continuum models