Reconstruction of Phase Dynamics from Macroscopic Observations Based on Linear and Nonlinear Response Theories

TL;DR

This paper introduces a new method to reconstruct phase dynamics equations from macroscopic responses to weak inputs, utilizing linear and nonlinear response theories, applicable to various coupled oscillator systems including neural networks.

Contribution

It develops a novel approach linking macroscopic responses to system parameters, including time delays, without invasive microscopic measurements.

Findings

Successfully applied to Hodgkin-Huxley neuron models with time delay

Derives formulas connecting responses with system parameters

Broad applicability in different fields

Abstract

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the responses with the system parameters including the time delay in interactions. We examine our method by applying it to two phase models, one of which describes a mean-field network of the Hodgkin--Huxley type neurons with a nonzero time delay. The method does not require much invasiveness nor microscopic observations, and these advantages highlight its broad applicability in various fields.