Self-sustained irregular activity in an ensemble of neural oscillators

Abstract

An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is observed. The "synchronised phase", which emerges upon increasing the coupling strength, is characterized by highly-irregular fluctuations: a time-series analysis reveals that the dynamics of the order parameter is indeed high-dimensional. The complex dynamics appears to be the result of the non-perturbative action of a suitably shaped phase-response curve. Such mechanism differs from the often invoked balance between excitation and inhibition and might provide an alternative basis to account for the self-sustained brain activity in the resting state. The potential interest of this dynamical regime is further strengthened by its (microscopic) linear stability, which makes it quite suited for computational tasks. The overall study has been performed by combining analytical and numerical studies, starting from the linear stability analysis of the asynchronous regime, to include the Fourier analysis of the Kuramoto order parameter, the computation of various types of Lyapunov exponents, and a microscopic study of the inter-spike intervals.

arXiv comment11 pages, 10 figures

References in corpus (22)

• Practical implementation of nonlinear time series methods: The TISEAN package
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Time Delay in the Kuramoto Model of Coupled Oscillators
• Macroscopic description for networks of spiking neurons
• Weak chimeras in minimal networks of coupled phase oscillators
• Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
• Synchronization in a System of Globally Coupled Oscillators with Time Delay
• Low-dimensional dynamics of populations of pulse-coupled oscillators
• Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State
• Stable Irregular Dynamics in Complex Neural Networks
• Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling
• Desynchronization in diluted neural networks
• Desynchronized stable states in diluted neural networks
• Collective behavior of heterogeneous neural networks
• Stable chaos
• A proof of the Kuramoto conjecture for a bifurcation structure of the infinite dimensional Kuramoto model
• Collective oscillations in disordered neural networks
• Stability and bifurcation for the Kuramoto model
• Noiseless Collective Motion out of Noisy Chaos
• On the equivalence of phase-oscillator and integrate-and-fire models
• The Kuramoto model of coupled oscillators with a bi-harmonic coupling function
• Collective Lyapunov modes

Cited by in corpus (17)

• Coupling functions: Universal insights into dynamical interaction mechanisms
• Chaos in generically coupled phase oscillator networks with nonpairwise interactions
• From quasiperiodic partial synchronization to collective chaos in populations of inhibitory neurons with delay
• Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons
• Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling
• Cross frequency coupling in next generation inhibitory neural mass models
• Death and rebirth of neural activity in sparse inhibitory networks
• Phase-Amplitude Coupling in Neuronal Oscillator Networks
• Chaos and correlated avalanches in excitatory neural networks with synaptic plasticity
• Quantitative and qualitative analysis of asynchronous neural activity
• On the interpretation of Dirac $\delta$ pulses in differential equations for phase oscillators
• Discrete synaptic events induce global oscillations in balanced neural networks
• Collective dynamics in the presence of finite-width pulses
• A robust balancing mechanism for spiking neural networks
• Synaptic shot-noise triggers fast and slow global oscillations in balanced neural networks
• Dynamics and computation in mixed networks containing neurons that accelerate towards spiking
• Resonant features in a forced population of excitatory neurons