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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

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Published on: March 2, 2015

Transient Turing patterns in a neural field model.

A J Elvin¹, C R Laing, M G Roberts

¹Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, NSMC, Auckland, New Zealand. a.elvin@math.auckland.ac.nz

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 5, 2009

Summary

This summary is machine-generated.

We studied Turing bifurcations in neural field models. The study reveals that pattern stability depends on the proximity of bifurcation points, leading to transient patterns similar to type-I intermittency.

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Area of Science:

Computational Neuroscience
Mathematical Biology
Pattern Formation

Background:

Neural field models are used to study emergent patterns in biological systems.
Turing bifurcations are a key mechanism for pattern formation in reaction-diffusion systems.

Purpose of the Study:

To investigate the dynamics of Turing bifurcations in a one-dimensional neural field model.
To understand the conditions leading to stable versus transient Turing patterns.

Main Methods:

Analysis of a one-dimensional neural field model.
Examination of parameter space to identify bifurcation points.
Comparison of transient pattern duration with type-I intermittency scaling.

Main Results:

The stability of Turing patterns is determined by the relative positions of the saddle-node bifurcation and the Turing bifurcation point.
Transient Turing patterns were observed, with durations scaling similarly to type-I intermittency.
Similar transient behaviors were found in two-dimensional models.

Conclusions:

The interplay between different bifurcation types dictates pattern stability in neural fields.
Transient patterns in neural fields exhibit universal scaling behaviors.
These findings enhance our understanding of pattern formation mechanisms in neural systems.