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Analysis of neural excitability and oscillations
Dynamic patterns: The self-organization of brain and behavior
- G. Ermentrout
- 1 March 1997
Mathematical foundations of neuroscience
The Hodgkin-Huxley Equations are applied to the model of Neuronal Networks to describe the “spatially distributed” networks.
Gamma rhythms and beta rhythms have different synchronization properties.
- N. Kopell, G. Ermentrout, M. Whittington, R. Traub
- BiologyProceedings of the National Academy of Sciences…
- 15 February 2000
A simplified model is used to show that the different rhythms in the CA1 region of the hippocampus employ different dynamical mechanisms to synchronize, based on different ionic currents, which are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are use for higher level interactions involving more distant structures.
Parabolic bursting in an excitable system coupled with a slow oscillation
We investigate the interaction of an excitable system with a slow oscillation. Under robust and general assumptions compatible with the more stringent assumptions usually made about excitable…
Existence and uniqueness of travelling waves for a neural network
Synopsis A one-dimensional scalar neural network with two stable steady states is analysed. It is shown that there exists a unique monotone travelling wave front which joins the two stable states.…
Multiple pulse interactions and averaging in systems of coupled neural oscillators
Oscillators coupled strongly are capable of complicated behavior which may be pathological for biological control systems. Nevertheless, strong coupling may be needed to prevent asynchrony. We…
Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
A chain of $n + 1$ weakly coupled oscillators with a linear gradient in natural frequencies is shown to exhibit “frequency plateaus,” or sequences of oscillators having the same frequency, with a…
Traveling Electrical Waves in Cortex Insights from Phase Dynamics and Speculation on a Computational Role
A mathematical theory of visual hallucination patterns
Bifurcation theory and group theory are used to demonstrate the existence of a variety of doublyperiodic patterns, hexagons, rolls, etc., as solutions to the field equations for the net activity.