Nonlinear analysis of periodic waves in a neural field model
S Budzinskiy1, A Beuter2, V Volpert3
1Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia.
Chaos (Woodbury, N.Y.)
|September 3, 2020
Summary
Brain activity involves electrical waves that synchronize neural activity. This study models these traveling waves, suggesting local brain signal origins, or epicenters, initiate wave propagation.
Area of Science:
- Neuroscience
- Computational Neuroscience
- Mathematical Biology
Background:
- Brain activity, including motor, visual, and language functions, involves periodic electrical potential waves in the cortex.
- These traveling waves may synchronize neural activity and modulate cortical excitability.
- Related phenomena include cortical spreading depression, observed in migraine, stroke, and traumatic brain injury.
Purpose of the Study:
- To explore the role of neural signal epicenters in initiating brain wave propagation.
- To investigate the emergence and stability of traveling and standing waves in neural activity.
Main Methods:
- Utilized a neural field model with two nonlinear integrodifferential equations.
- Modeled excitatory and inhibitory neuronal populations with symmetric connectivity.
- Employed bifurcation analysis to study wave emergence and stability.
Main Results:
- Identified conditions for the emergence of periodic traveling waves and standing oscillations.
- Demonstrated that local oscillations, indicative of epicenters, can initiate wave propagation.
- Analyzed the stability of stationary, spatially homogeneous solutions.
Conclusions:
- Neural field models can replicate traveling and standing brain waves.
- Local neural activity epicenters likely play a crucial role in initiating cortical waves.
- Findings contribute to understanding brain dynamics in health and disease.
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