On the Phase Reduction and Response Dynamics of Neural Oscillator Populations

Authors:
Eric Brown;Jeff Moehlis;Philip Holmes
Affiliations:
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, U.S.A.;Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, U.S.A.;Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, U.S.A.
Venue:
Neural Computation
Year:
2004

Citing 17
Cited 19

Oscillator death in systems of coupled neural oscillators

SIAM Journal on Applied Mathematics
Analysis of neural excitability and oscillations

Methods in neuronal modeling
Synchrony in excitatory neural networks

Neural Computation
What matters in neuronal locking?

Neural Computation
Weakly connected neural networks

Weakly connected neural networks
Mathematical physiology

Mathematical physiology
Elements of applied bifurcation theory (2nd ed.)

Elements of applied bifurcation theory (2nd ed.)
From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

Physica D
Phase equations for relaxation oscillators

SIAM Journal on Applied Mathematics
Simulating, Analyzing, and Animating Dynamical Systems: A Guide Toi Xppaut for Researchers and Students

Simulating, Analyzing, and Animating Dynamical Systems: A Guide Toi Xppaut for Researchers and Students
Spiking Neuron Models: An Introduction

Spiking Neuron Models: An Introduction
A population study of integrate-and-fire-or-burst neurons

Neural Computation
Dynamics of the firing probability of noisy integrate-and-fire neurons

Neural Computation
Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking

Neural Computation
Dynamics of Strongly Coupled Spiking Neurons

Neural Computation
Type i membranes, phase resetting curves, and synchrony

Neural Computation
Neural mechanisms of scene segmentation: recordings from the visual cortex suggest basic circuits for linking field models

IEEE Transactions on Neural Networks

Computation of the Phase Response Curve: A Direct Numerical Approach

Neural Computation
Critical Analysis of Dimension Reduction by a Moment Closure Method in a Population Density Approach to Neural Network Modeling

Neural Computation
Type i and type ii neuron models are selectively driven by differential stimulus features

Neural Computation
Spike train statistics and dynamics with synaptic input from any renewal process: A population density approach

Neural Computation
Self-organizing sync in a robotic swarm: a dynamical system view

IEEE Transactions on Evolutionary Computation
Computing quadratic approximations for the isochrons of oscillators: a general theory and advanced numerical methods

Proceedings of the 2009 International Conference on Computer-Aided Design
Clustering limit cycle oscillators by spectral analysis of the synchronisation matrix with an additional phase sensitive rotation

ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Convergence analysis of a numerical method to solve the adjoint linearized periodic orbit equations

Applied Numerical Mathematics
Quadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods, and accurate phase computations

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Synaptic and intrinsic determinants of the phase resetting curve for weak coupling

Journal of Computational Neuroscience
Spike-timing-dependent plasticity and reliability optimization: The role of neuron dynamics

Neural Computation
A dynamical pattern recognition model of gamma activity in auditory cortex

Neural Networks
Phase response curves, delays and synchronization in MATLAB

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
The shape of phase-resetting curves in oscillators with a saddle node on an invariant circle bifurcation

Neural Computation
Minimum energy desynchronizing control for coupled neurons

Journal of Computational Neuroscience
Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators

Neural Computation
Functional identification of spike-processing neural circuits

Neural Computation
Linking dynamical and functional properties of intrinsically bursting neurons

Journal of Computational Neuroscience
Synchronization of delayed coupled neurons in presence of inhomogeneity

Journal of Computational Neuroscience

Quantified Score

Hi-index	0.00

Visualization

Abstract

Weundertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli. Recalling and extending results from the literature, we compute phase response curves (PRCs) valid near bifurcations to periodic firing for Hindmarsh-Rose, Hodgkin-Huxley, FitzHugh-Nagumo, and Morris-Lecar models, encompassing the four generic (codimension one) bifurcations. Phase density equations are then used to analyze the role of the bifurcation, and the resulting PRC, in responses to stimuli. In particular, we explore the interplay among stimulus duration, baseline firing frequency, and population-level response patterns. We interpret the results in terms of the signal processing measure of gain and discuss further applications and experimentally testable predictions.