Optimal network topologies for information transmission in active networks

Abstract

This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

20 pages, 12 figures

References in corpus (7)

• Synchronization in small-world systems
• Scale-free brain functional networks
• Universality in the synchronization of weighted random networks
• Evolutionary reconstruction of networks
• Complete chaotic synchronization in mutually coupled time-delay systems
• Transmission of Information in Active Networks
• Non-transitive maps in phase synchronization

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• Synaptic Plasticity and Spike Synchronisation in Neuronal Networks
• Inference of forex and stock-index financial networks based on the normalised mutual information rate
• Transmission of information and synchronization in a pair of coupled chaotic circuits: an experimental overview
• Production and Transfer of Energy and Information in Hamiltonian Systems
• Synchronization and Information Transmission in Spatio-Temporal Networks of Deformable Units
• Network inference combining mutual information rate and statistical tests
• Stability and Bifurcation Analysis of Coupled Fitzhugh-Nagumo Oscillators
• How complex a complex network of equal nodes can be?
• Network Mutual Information and Synchronization under Time Transformations