Towards a Protocol for Adaptive Dynamical Bayesian Inference: Case of Limit-Cycle Oscillators

Abstract

Several methods exist that allow the study of the interactions between dynamic systems in nature. Among them is the method of dynamic Bayesian inference, which allows reconstruction of a model that describes the interactions between different dynamical systems, based on the measured time series originating from these systems. Based on an investigation of a known system of two coupled phase oscillators, an algorithm for improving this method has been proposed, by adaptively determining two parameters that were previously arbitrarily selected – the time win-dow and the propagation parameter. This paper presents the results of the evaluation of the introduced algorithm on a second system of coupled oscillators - limit-cycle Poincaré oscillators in the presence of noise. The performed analysis confirmed the relevance of the proposed algorithm for improved model inference, which allows for a deeper understanding of the interactions described by the coupling functions of the dynamical systems.