Extended-GC swMATH ID: 38880 Software Authors: Grantcheng; Hong Cheng, David Cai, Douglas Zhou Description: Extended-GC: The extended Granger causality analysis for Hodgkin–Huxley neuronal models. How to extract directions of information flow in dynamical systems based on empirical data remains a key challenge. The Granger causality (GC) analysis has been identified as a powerful method to achieve this capability. However, the framework of the GC theory requires that the dynamics of the investigated system can be statistically linearized; i.e., the dynamics can be effectively modeled by linear regressive processes. Under such conditions, the causal connectivity can be directly mapped to the structural connectivity that mediates physical interactions within the system. However, for nonlinear dynamical systems such as the Hodgkin–Huxley (HH) neuronal circuit, the validity of the GC analysis has yet been addressed; namely, whether the constructed causal connectivity is still identical to the synaptic connectivity between neurons remains unknown. In this work, we apply the nonlinear extension of the GC analysis, i.e., the extended GC analysis, to the voltage time series obtained by evolving the HH neuronal network. In addition, we add a certain amount of measurement or observational noise to the time series to take into account the realistic situation in data acquisition in the experiment. Our numerical results indicate that the causal connectivity obtained through the extended GC analysis is consistent with the underlying synaptic connectivity of the system. This consistency is also insensitive to dynamical regimes, e.g., a chaotic or non-chaotic regime. Since the extended GC analysis could in principle be applied to any nonlinear dynamical system as long as its attractor is low dimensional, our results may potentially be extended to the GC analysis in other settings. Homepage: https://aip.scitation.org/doi/abs/10.1063/5.0006349 Source Code: https://github.com/Grantcheng/Extended-GC Dependencies: Matlab Related Software: Brain Connectivity Toolbox; GitHub; IOTA Cited in: 1 Publication Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The extended Granger causality analysis for Hodgkin-Huxley neuronal models. Zbl 1451.92067Cheng, Hong; Cai, David; Zhou, Douglas 2020 Cited by 3 Authors 1 Cai, David 1 Cheng, Hong 1 Zhou, Douglas Cited in 1 Serial 1 Chaos Cited in 2 Fields 1 Dynamical systems and ergodic theory (37-XX) 1 Biology and other natural sciences (92-XX) Citations by Year