Abstract
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. Common approaches to study cluster synchronization in networks of coupled oscillators ground on simplifying assumptions, which often neglect key biological features of neuron networks. Here we propose a general framework to study presence and stability of synchronous clusters in more realistic models of neuron networks, characterized by the presence of delays, different kinds of neurons and synapses. Application of this framework to two examples with different size and features (the directed network of the macaque cerebral cortex and the swim central pattern generator of a mollusc) provides an interpretation key to explain known functional mechanisms emerging from the combination of anatomy and neuron dynamics. The cluster synchronization analysis is carried out also by changing parameters and studying bifurcations. Despite some modeling simplifications in one of the examples, the obtained results are in good agreement with previously reported biological data.
Highlights
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing
K=1 j=1 where xi ∈ Rn is the n-dimensional state vector of the i-th neuron, fi : Rn → Rn is the vector field of the isolated i-th neuron, σ k ∈ R is the coupling strength of the k-th kind of link, Ak is the possibly weighted and directed coupling matrix that describes the connectivity of the network with respect to the k-th kind of link, for which the interaction between two generic cells i and j is described by the nonlinear function hk : Rn × Rn → Rn, and δk is the axon transmission delay characteristic of the k-th kind of link
We assume that the synaptic coupling influences only the dynamics of Vi and not of the other state variables contained in xi : the first component of the vector hk(·) is a scalar function ak(Vi(t), xj(t − δk)) and the remaining components are null
Summary
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. This notwithstanding, recent efforts have been devoted to apply nonlinear dynamics concepts and network theory to the neuroscience c ontext[1,7] This is done by resorting to deterministic models (which is a first-order simplification) and studying the presence and the stability of synchronized clusters in networks based on one or more assumptions (second-order simplifications), such as identical neurons/synapses, weak interactions, absence of delays, or undirected/diffusive connections. We successfully apply our approach to two neuron networks on different scales: the first one is the small-scale central pattern generator responsible for swim motion of the nudibranch mollusc Dendronotus iris; the second one is the large-scale cortical connectivity network of the macaque, which describes anatomical connections among different cortical areas In both cases, the analysis is carried out changing some significant network parameters (following real experiments that we use as benchmarks), by exploiting bifurcation analysis combined with the proposed CS analysis. The obtained results are in agreement with previously reported biological behaviors for both case studies, indicating that the proposed analysis can be useful to study real neuron networks, to predict the existence of stable synchronous clusters, and to perform virtual experiments in view of better focused real experiments
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