Macroscopic Description for Networks of Spiking Neurons

2015/06/19 by Ernest Montbrió, Diego Pazó, Alex Roxin · 11 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · Physics and Astronomy · #Complex system #Differential (mechanical device) #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Ordinary differential equation #Spiking neural network #cond-mat.dis-nn #nlin.AO #nlin.CD #q-bio.NC #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physrevx.5.021028

published as Phys. Rev. X 5, 021028 (2015)

openalex publication_date 2015/06/19 · arxiv created 2015/06/22 · arxiv updated 2015/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Understanding memory and decision making in the human brain requires generating models of how neurons fire. Using ordinary differential equations, researchers formulate an exact firing rate description for an ensemble of spiking neurons.

Citations

• Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons
• A quantitative description of membrane current and its application to conduction and excitation in nerve
• Time structure of the activity in neural network models
• Long time evolution of phase oscillator systems
• Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: bifurcation of the order function
• Constants of motion for superconducting Josephson arrays
• Waves, bumps, and patterns in neural field theories
• Temporal binding and the neural correlates of sensory awareness
• Neurons with graded response have collective computational properties like those of two-state neurons.
• Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory

Cited by

• Slow spectral dynamics of shot noise in the Kuramoto model: the role of microscopic regularity
• Dissecting emerging slow rhythms in delay-coupled neural oscillators
• Shot noise generated by subpopulations of neural networks
• Symmetry breaking and high-dimensional chaos in sparse random networks of exact firing rate models
• Dynamic solutions of next generation neural field models with delays
• Parameter and hidden-state inference in mean-field models from partial observations of finite-size neural networks
• Compressing Complexity: A Critical Synthesis of Structural, Analytical, and Data-Driven Dimensionality Reduction in Dynamical Networks
• Synchronization of coupled active rotators by common noise
• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
• Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott–Antonsen theory
• Sparse optimization of mutual synchronization in collectively oscillating networks

Related

• Statistical Field Theory and Networks of Spiking Neurons
• Constructing precisely computing networks with biophysical spiking neurons
• Minimizing information loss reduces spiking neuronal networks to differential equations
• Bifurcation analysis of the dynamics of interacting populations of spiking networks
• Computational modeling of neuronal networks