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Pattern formation in multiplex networks.

ABSTRACT: The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates heterogeneous patterns with significant differences from those observed in single-layer networks. Remarkably, diffusion-induced instability can occur even if the two species have the same mobility rates; condition which can never destabilize single-layer networks. The instability condition is revealed using perturbation theory and expressed by a combination of degrees in the different layers. Our theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.

SUBMITTER: Kouvaris NE

PROVIDER: S-EPMC4455352 | biostudies-literature | 2015 Jun

REPOSITORIES: biostudies-literature

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Pattern formation in multiplex networks.

Kouvaris Nikos E NE Hata Shigefumi S Guilera Albert Díaz- AD

Scientific reports 20150604

The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their ow ...[more]

PMID: 26042606

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Project description:The communication of neurons is primarily maintained by synapses, which play a crucial role in the functioning of the nervous system. Therefore, synaptic failure may critically impair information processing in the brain and may underlie many neurodegenerative diseases. A number of studies have suggested that synaptic failure may preferentially target neurons with high connectivity (i.e., network hubs). As a result, the activity of these highly connected neurons can be significantly affected. It has been speculated that anesthetics regulate conscious state by affecting synaptic transmission at these network hubs and subsequently reducing overall coherence in the network activity. In addition, hubs in cortical networks are shown to be more vulnerable to amyloid deposition because of their higher activity within the network, causing decrease in coherence patterns and eventually Alzheimer's disease (AD). Here, we investigate how synaptic failure can affect spatio-temporal dynamics of scale free networks, having a power law scaling of number of connections per neuron - a relatively few neurons (hubs) with a lot of emanating or incoming connections and many cells with low connectivity. We studied two types of synaptic failure: activity-independent and targeted, activity-dependent synaptic failure. We defined scale-free network structures based on the dominating direction of the connections at the hub neurons: incoming and outgoing. We found that the two structures have significantly different dynamical properties. We show that synaptic failure may not only lead to the loss of coherence but unintuitively also can facilitate its emergence. We show that this is because activity-dependent synaptic failure homogenizes the activity levels in the network creating a dynamical substrate for the observed coherence increase. Obtained results may lead to better understanding of changes in large-scale pattern formation during progression of neuro-degenerative diseases targeting synaptic transmission.

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Pattern formation in multiplex networks.

Publications

Pattern formation in multiplex networks.

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