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Origin of coherent structures in a discrete chaotic medium
M I Rabinovich1, J J Torres, P Varona
1Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA.
Summary
We found that synchronized chaotic neurons can form ordered structures in a discrete medium. This ordering is driven by the mean field effect and controlled by fast chaotic pulsations.
Area of Science:
- Computational Neuroscience
- Complex Systems
Background:
- Neurons exhibit chaotic dynamics with fast and slow oscillations.
- Interactions in large neural networks can lead to emergent ordered structures.
Purpose of the Study:
- To investigate the origin of ordered structures in a discrete nonequilibrium medium of chaotic neurons.
- To understand the role of synchronization and mean field effects in emergent order.
Main Methods:
- Modeling a large lattice of locally interacting Hindmarsh-Rose chaotic neurons.
- Analyzing the collective dynamics and synchronization of neuron groups.
- Introducing and studying the behavior of "coarse grains" (clusters of neurons with periodic averaged behavior).
Main Results:
- Ordered structures emerge from the interplay of fast and slow chaotic oscillations.
- A periodic average dynamics arises in synchronized neuron groups due to the mean field.
- Spatially ordered patterns in coarse grains are controlled by the intensity of fast chaotic pulsations.
Conclusions:
- The mean field synchronization of chaotic neurons is a key mechanism for generating order.
- "Coarse graining" provides a useful framework for studying large-scale neural dynamics.
- Fast chaotic pulsations play a crucial role in controlling emergent spatial order.