2020/06/07 by Benjamin Ambrosio, Lai-Sang Young, Ambrosio, Benjamin +1
Computer Science · Neuroscience · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Neural Networks and Applications #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2006.04039
openalex publication_date 2020/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The brain produces rhythms in a variety of frequency bands. Some are likely\nby-products of neuronal processes; others are thought to be top-down. Produced\nentirely naturally, these rhythms have clearly recognizable beats, but they are\nvery far from periodic in the sense of mathematics. They produce signals that\nare broad-band, episodic, wandering in magnitude, in frequency and in phase;\nthe rhythm comes and goes, degrading and regenerating. Rhythms with these\ncharacteristics do not match standard dynamical systems paradigms of\nperiodicity, quasi-periodicity, or periodic motion in the presence of a\nBrownian noise. Thus far they have been satisfactorily reproduced only using\nnetworks of hundreds of integrate-and-fire neurons. In this paper, we tackle\nthe mathematical question of whether signals with these properties can be\ngenerated from simpler dynamical systems. Using an ODE with two variables\ninspired by the FitzHugh-Nagumo model, and varying randomly three parameters\nthat control the magnitude, frequency and degree of degradation, we were able\nto replicate the qualitative characteristics of these natural brain rhythms.\nViewing the two variables as Excitatory and Inhibitory conductances of a\ntypical neuron in a local population, our model produces results that closely\nresemble gamma-band activity in real cortex, including the moment-to-moment\nbalancing of E and I-currents seen in experiments.\n