Excitable elements controlled by noise and network structure

Abstract

We study collective dynamics of complex networks of stochastic excitable elements, active rotators. In the thermodynamic limit of infinite number of elements, we apply a mean-field theory for the network and then use a Gaussian approximation to obtain a closed set of deterministic differential equations. These equations govern the order parameters of the network. We find that a uniform decrease in the number of connections per element in a homogeneous network merely shifts the bifurcation thresholds without producing qualitative changes in the network dynamics. In contrast, heterogeneity in the number of connections leads to bifurcations in the excitable regime. In particular we show that a critical value of noise intensity for the saddle-node bifurcation decreases with growing connectivity variance. The corresponding critical values for the onset of global oscillations (Hopf bifurcation) show a non-monotone dependency on the structural heterogeneity, displaying a minimum at moderate connectivity variances.

13 pages, 6 figures

References in corpus (7)

• Synchronization in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Stability diagram for the forced Kuramoto model
• Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
• Connectivity-Driven Coherence in Complex Networks
• Global firing induced by network disorder in ensembles of active rotators
• Networks of noisy oscillators with correlated degree and frequency dispersion

Cited by in corpus (19)

• The Kuramoto model in complex networks
• Approximate solution to the stochastic Kuramoto model
• Does the brain behave like a (complex) network? I. Dynamics
• Activation process in excitable systems with multiple noise sources: Large number of units
• Collective dynamics in two populations of noisy oscillators with asymmetric interactions
• Synchronization of coupled active rotators by common noise
• Propagation failure of excitation waves on trees and random networks
• Two Scenarios for the Onset and Suppression of Collective Oscillations in Heterogeneous Populations of Active Rotators
• Emergence and coherence of oscillations in star networks of stochastic excitable elements
• Emergent stochastic oscillations and signal detection in tree networks of excitable elements
• Functional control of network dynamics using designed Laplacian spectra
• Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
• Delay-induced stochastic bursting in excitable noisy systems
• Dynamics of oscillator populations with disorder in the coupling phase shifts
• Mean-field dynamics of a population of stochastic map neurons
• Information-theoretic description of a feedback-control Kuramoto model
• Gaussian theory for spatially distributed self-propelled particles
• Tristable and multiple bistable activity in complex random binary networks of two-state units
• Regular graphs maximize the variability of random neural networks