Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models

The Journal of Mathematical Neuroscience - Tập 9 - Trang 1-11 - 2019
Cheng Ly1, Woodrow L. Shew2, Andrea K. Barreiro3
1Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, USA
2Department of Physics, University of Arkansas, Fayetteville, USA
3Department of Mathematics, Southern Methodist University, Dallas, USA

Tóm tắt

Understanding nervous system function requires careful study of transient (non-equilibrium) neural response to rapidly changing, noisy input from the outside world. Such neural response results from dynamic interactions among multiple, heterogeneous brain regions. Realistic modeling of these large networks requires enormous computational resources, especially when high-dimensional parameter spaces are considered. By assuming quasi-steady-state activity, one can neglect the complex temporal dynamics; however, in many cases the quasi-steady-state assumption fails. Here, we develop a new reduction method for a general heterogeneous firing-rate model receiving background correlated noisy inputs that accurately handles highly non-equilibrium statistics and interactions of heterogeneous cells. Our method involves solving an efficient set of nonlinear ODEs, rather than time-consuming Monte Carlo simulations or high-dimensional PDEs, and it captures the entire set of first and second order statistics while allowing significant heterogeneity in all model parameters.

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The Journal of Mathematical Neuroscience

Tập 9

1-11

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