Quantitative Characteristics of Causality in a Classical Problem of the Theory of Oscillations

Abstract

Within the formalism of dynamic effects of directional coupling, or dynamic causal effects (DCEs), the relations between modern quantifiers of coupling between oscillatory systems (transfer entropy, Granger–Geweke causality spectrum, spectral DCEs, etc.) and the classical notions of the oscillation theory—namely, the concepts of “coupling” and “coupledness” by Mandelstam—are studied for an exemplary system of two linear dissipative stochastic oscillators. It is shown that the “coupledness” has two different meanings, which are expressed via different DCEs. A whole set of DCEs appears to be a detailed expression of the coupledness concept and provides a more accurate description of the different dynamic aspects of coupling.