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Mechanisms for Frequency Control in Neuronal Competition Models.

Rodica Curtu¹, Asya Shpiro, Nava Rubin

¹Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, and Transilvania University of Brasov, Romania ( rodica-curtu@uiowa.edu ).

SIAM Journal on Applied Dynamical Systems

|September 28, 2011

Summary

This study analyzes a two-population neural network model with mutual inhibition and spike frequency adaptation. It reveals how input strength controls network states, including oscillations and winner-take-all dynamics, through Hopf bifurcations.

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Area of Science:

Computational Neuroscience
Theoretical Neuroscience
Dynamical Systems Theory

Background:

Neural networks with mutual inhibition are fundamental to understanding brain function.
Spike frequency adaptation (SFA) is a crucial intrinsic neuronal property influencing network dynamics.
Investigating how external input shapes network states is key to neural computation.

Purpose of the Study:

To analytically investigate a firing rate model of a two-population network with mutual inhibition and SFA.
To characterize the conditions leading to different dynamical states: steady states, oscillations, and bistability (winner-take-all).
To elucidate the mechanisms underlying oscillatory behavior and their dependence on input strength.

Main Methods:

Analytical investigation of a two-population firing rate model.
Mathematical analysis of system dynamics, including Hopf bifurcations.
Characterization of nonmonotonic dependence of oscillation period on input strength.

Main Results:

Oscillations emerge via supercritical Hopf bifurcations and are antiphase.
Oscillation period exhibits nonmonotonic dependence on input strength, linked to 'release' and 'escape' mechanisms.
Conditions for release, escape, and winner-take-all behavior are characterized, especially in the slow feedback limit.

Conclusions:

The model analytically demonstrates how mutual inhibition and SFA generate diverse network dynamics.
Input strength is a critical parameter controlling transitions between steady states, oscillations, and bistability.
The findings provide insights into the mechanisms of neural oscillations and state transitions in biological networks.