Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks

Stroud, Jake P.; Barahona, Mauricio; Pereira, Tiago

doi:10.1007/978-3-319-17037-4_4

Cited by 7 publications

(8 citation statements)

References 30 publications

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“…Some papers showed that the cat array has a high hierarchical level [10,35]. This enables the formation of hierarchical synchronization [36,37,38]. We verify that the coherent regions in the chimera-like states are related to synchronisation between the neurons of the same connectional group of areas, mainly in auditory and somatosensorymotor.…”

Section: Matching Indexsupporting

confidence: 67%

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Chimera-like states in a neuronal network model of the cat brain

Santos

Szezech

Borges

et al. 2017

Chaos, Solitons & Fractals

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Neuronal systems have been modelled by complex networks in different description levels. Recently, it has been verified that networks can simultaneously exhibit one coherent and other incoherent domain, known as chimera states. In this work, we study the existence of chimera-like states in a network considering the connectivity matrix based on the cat cerebral cortex. The cerebral cortex of the cat can be separated in 65 cortical areas organised into the four cognitive regions: visual, auditory, somatosensory-motor and frontolimbic. We consider a network where the local dynamics is given by the Hindmarsh-Rose model. The Hindmarsh-Rose equations are a well known model of neuronal activity that has been considered to simulate membrane potential in neuron. Here, we analyse under which conditions chimera-like states are present, as well as the affects induced by intensity of coupling on them. We identify two different kinds of chimera-like states: spiking chimera-like with desynchronised spikes, and bursting chimera-like with desynchronised bursts. Moreover, we find that chimera-like states with desynchronised bursts are more robust to neuronal noise than with desynchronised spikes.

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Section: Matching Indexsupporting

confidence: 67%

“…In future works, we plan a deeper analysis of the root cause of the chimera-like phenomenon in the cat network. It will be analysed the instability of synchronisation in terms of the master stability function [38,45].…”

Section: Discussionmentioning

confidence: 99%

Chimera-like states in a neuronal network model of the cat brain

Santos

Szezech

Borges

et al. 2017

Chaos, Solitons & Fractals

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“…1) will, in general, affect the characteristics of the network activity; in fact, this is the premise of our study. The problem of systematically predicting network activity from local properties – the notorious structure-function problem – is currently unsolved, although this is an active area of research (see [57] for instance). The purpose of this paper is to propose a practical method allowing to search for a desired network behaviour in a reasonable time, by manipulating a relatively small number of parameters.…”

Section: Resultsmentioning

confidence: 99%

Bayesian Optimisation of Large-Scale Biophysical Networks

et al. 2018

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The relationship between structure and function in the human brain is well established, but not yet well characterised. Large-scale biophysical models allow us to investigate this relationship, by leveraging structural information (e.g. derived from diffusion tractography) in order to couple dynamical models of local neuronal activity into networks of interacting regions distributed across the cortex. In practice however, these models are difficult to parametrise, and their simulation is often delicate and computationally expensive. This undermines the experimental aspect of scientific modelling, and stands in the way of comparing different parametrisations, network architectures, or models in general, with confidence. Here, we advocate the use of Bayesian optimisation for assessing the capabilities of biophysical network models, given a set of desired properties (e.g. band-specific functional connectivity); and in turn the use of this assessment as a principled basis for incremental modelling and model comparison. We adapt an optimisation method designed to cope with costly, high-dimensional, non-convex problems, and demonstrate its use and effectiveness. Using five parameters controlling key aspects of our model, we find that this method is able to converge to regions of high functional similarity with real MEG data, with very few samples given the number of parameters, without getting stuck in local extrema, and while building and exploiting a map of uncertainty defined smoothly across the parameter space. We compare the results obtained using different methods of structural connectivity estimation from diffusion tractography, and find that one method leads to better simulations.

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“…However, the star graph has an exceptional number of zero eigenvalues of L ( G ), N − 2 in fact. The number of zero eigenvalues of L ( G ) quantifies the number of connections in a graph and it has been used to assess robustness and synchronizability of networks [153,154].…”

Section: Hamiltonian Design For Coherencementioning

confidence: 99%

Polaritons and excitons: Hamiltonian design for enhanced coherence

Scholes

2020

Proc. R. Soc. A.

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The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian—connections between sites (or molecules) made by electronic coupling—is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.

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Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks

Cited by 7 publications

References 30 publications

Chimera-like states in a neuronal network model of the cat brain

Chimera-like states in a neuronal network model of the cat brain

Bayesian Optimisation of Large-Scale Biophysical Networks

Polaritons and excitons: Hamiltonian design for enhanced coherence

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