Macroscopic complexity from an autonomous network of networks of theta neurons.
Date
2014-11-18
Authors
Luke, Tanushree B.
Barreto, Ernest
So, Paul
Journal Title
Journal ISSN
Volume Title
Publisher
Frontiers Media
Abstract
We examine the emergence of collective dynamical structures and complexity in a network of interacting populations of neuronal oscillators. Each population consists of a heterogeneous collection of globally-coupled theta neurons, which are a canonical representation of Type-1 neurons. For simplicity, the populations are arranged in a fully autonomous driver-response configuration, and we obtain a full description of the asymptotic macroscopic dynamics of this network. We find that the collective macroscopic behavior of the response population can exhibit equilibrium and limit cycle states, multistability, quasiperiodicity, and chaos, and we obtain detailed bifurcation diagrams that clarify the transitions between these macrostates. Furthermore, we show that despite the complexity that emerges, it is possible to understand the complicated dynamical structure of this system by building on the understanding of the collective behavior of a single population of theta neurons. This work is a first step in the construction of a mathematically-tractable network-of-networks representation of neuronal network dynamics.
Description
Keywords
Theta neuron, Type-I neuron, Hierarchical network, Neural field, Macroscopic behavior, Coherence, Synchrony, Chaos
Citation
Luke TB, Barreto E and So P (2014) Macroscopic complexity from an autonomous network of networks of theta neurons. Front. Comput. Neurosci. 8:145. doi: 10.3389/fncom.2014.00145