The research of the group is focused on developing time series analysis methods based on the framework of nonlinear dynamics and information theory and applying them to experimental data. Oscillatory systems are a major object of interest as they are abundant in nature and some of their properties can be exploited to simplify the analysis process, for example consideration of the phase dynamics of the interacting systems.
Roughly, the researched methods can be separated into those concerning only a single time series, two time series and more than two time series.
Univariate analysis is concerned with analysing a single time series. The main problem is to characterize the time series itself and make inferences about the underlying system. Some important questions concern:
- the linearity or nonlinearity of the system,
- the complexity of the system,
- the level of determinism inherent in the system.
Bivariate analysis focuses on analyzing interactions of two systems at a time. A rich spectrum of interactions arises form this seemingly simple situation including various forms of synchronization and directional influence:
- generalized or lag synchronization,
- phase synchronization,
- drive-response or master-slave coupling,
- bidirectional coupling.
Multivariate analysis is concerned with finding communities in networks, analyzing complex network structures and estimating association levels between participating systems.