Coherent oscillations in balanced neural networks driven by endogenous fluctuations

Area of Science:

• Computational neuroscience
• Theoretical neuroscience
• Complex systems

Background:

• Balanced networks of spiking neurons are crucial for brain function.
• Understanding emergent dynamics in these networks is a key challenge.
• Previous models often simplify neuron dynamics or connectivity.

Purpose of the Study:

• To analyze dynamical regimes in balanced networks of quadratic integrate-and-fire neurons.
• To compare numerical simulations with a mean-field Fokker-Planck equation (FPE) model.
• To investigate the impact of in-degree distribution (homogeneous vs. heterogeneous) on network dynamics.

Main Methods:

• Numerical simulations of sparse balanced networks with identical quadratic integrate-and-fire neurons.
• Development and application of a self-consistent Fokker-Planck equation (FPE) mean-field model.
• Analysis of network behavior under varying parameter values, including connectivity and input current.
• Investigation of low-dimensional reductions of the FPE using circular cumulants.

Main Results:

• Spontaneous emergence of asynchronous or periodic oscillatory regimes depending on parameter values.
• FPE model accurately reproduces asynchronous dynamics, particularly with Poissonian or renewal input.
• Identification of mean-driven and fluctuation-driven balanced regimes via an exact mean firing rate solution.
• Two cumulants effectively capture network transition scenarios.
• Mean-field models successfully predict periodic collective oscillations in both homogeneous and heterogeneous networks.

Conclusions:

• The Fokker-Planck equation provides a robust framework for understanding emergent dynamics in balanced neural networks.
• Network behavior transitions between asynchronous and oscillatory states are well-described by mean-field theory.
• In-degree distribution and structural heterogeneity play significant roles in shaping network dynamics.