Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems

Abstract

We study stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. Diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed in the course of this transition. In order to understand details and mechanisms of noise-induced dynamics we consider a thermodynamic limit $N\to \infty$ of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In the Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.

References in corpus (8)

• Brownian motors: noisy transport far from equilibrium
• Stochastic Resonance in Ion Channels Characterized by Information Theory
• Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model
• Channel noise and synchronization in excitable membranes
• Macroscopic limit cycle via pure noise-induced phase transition
• Coupled three-state oscillators
• Switching Time Statistics for Driven Neuron Models: Analytic Expressions versus Numerics
• Dynamical mean-field theory of noisy spiking neuron ensembles: Application to the Hodgkin-Huxley model

Cited by in corpus (26)

• Extreme events in excitable systems and mechanisms of their generation
• Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines
• Approximate solution to the stochastic Kuramoto model
• Heterogeneous connections induce oscillations in large scale networks
• Voltage interval mappings for an elliptic bursting model
• Coherence resonance in neuronal populations: mean-field versus network model
• Activation process in excitable systems with multiple noise sources: Large number of units
• A minimal model for chaotic shear banding in shear-thickening fluids
• Excitable elements controlled by noise and network structure
• 100 Years of Brownian motion
• Noise-induced transitions in a double-well oscillator with nonlinear dissipation
• Diversity and noise effects in a model of homeostatic regulation of the sleep-wake cycle
• Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation
• Mean field approximation for noisy delay coupled excitable neurons
• Mean field approximation of two coupled populations of excitable units
• Noise-induced transitions in a double-well excitable oscillator
• Noise-induced Extreme Events in Hodgkin-Huxley Neural Networks
• Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
• Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units
• The Discrete Langevin Machine: Bridging the Gap Between Thermodynamic and Neuromorphic Systems
• Mean-field dynamics of a population of stochastic map neurons
• Heterogeneous noise-induced extreme events and synchronization in a globally coupled network of FitzHugh-Nagumo oscillators
• Exact potentials in multivariate Langevin equations
• Modeling rhythmic patterns in the hippocampus
• Analytical Approach to Noise Effects on Synchronization in a System of Coupled Excitable Elements
• Controlling Statistical Moments of Stochastic Dynamical Networks