2018/12/15 by Erik D. Fagerholm, Rosalyn Moran, Fagerholm, Erik D. +7
Computer Science · Neuroscience · #EEG and Brain-Computer Interfaces #FOS: Biological sciences #Neural Networks and Applications #Neural dynamics and brain function #Neuroscience and Neuropharmacology Research #Photoreceptor and optogenetics research #Quantitative Methods (q-bio.QM)
paper · pdf · doi:10.48550/arxiv.1812.06315
openalex publication_date 2018/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Models of coupled oscillators are useful in describing a wide variety of\nphenomena in physics, biology and economics. These models typically rest on the\npremise that the oscillators are weakly coupled, meaning that amplitudes can be\nassumed to be constant and dynamics can therefore be described purely in terms\nof phase differences. Whilst mathematically convenient, the restrictive nature\nof the weak coupling assumption can limit the explanatory power of these\nphase-coupled oscillator models. We therefore propose an extension to the\nweakly-coupled oscillator model that incorporates both amplitude and phase as\ndependent variables. We use the bilinear neuronal state equations of dynamic\ncausal modelling as a foundation in deriving coupled differential equations\nthat describe the activity of both weakly and strongly coupled oscillators. We\nshow that weakly-coupled oscillator models are inadequate in describing the\nprocesses underlying the temporally variable signals observed in a variety of\nsystems. We demonstrate that phase-coupled models perform well on simulations\nof weakly coupled systems but fail when connectivity is no longer weak. On the\nother hand, using Bayesian model selection, we show that our phase-amplitude\ncoupling model can describe non-weakly coupled systems more effectively despite\nthe added complexity associated with using amplitude as an extra dependent\nvariable. We demonstrate the advantage of our phase-amplitude model in the\ncontext of model-generated data, as well as of a simulation of inter-connected\npendula, neural local field potential recordings in rodents under anaesthesia\nand international economic gross domestic product data.\n