We briefly present lag sequential analysis for behavioral streams, a commonly used method in psychology for quantifying the relationships between two nominal time series. Cross recurrence quantification analysis (CRQA) is shown as an extension of this technique, and we exemplify this nominal application of CRQA to eye-movement data in human interaction. In addition, we demonstrate nominal CRQA ...

Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point x in a decreasing sequence of neighborhoods of another point y. It is proved that these recurrence indicators are a.e. greater or equal to the local dimension at y, then these recurrence indicators can be used to have a numerical upper bound on the local dimension of an invariant measure.

An ecosystem is a prototypical complex system, exhibiting a self-organised temporal dynamics, the characterisation and description of which is riddled with challenges. In this study, simulated ecosystems in the multi-species model WIST (Weather-driven, Individual-based, Spatially explicit, Terrestrial ecosystem model) are used as surrogates with which to explore and characterise the long-term d...

Complex spatio-temporal systems may exhibit irregular behaviors when driven far from equilibrium. Reaction-diffusion systems often lead to the formation of patterns and spatio-temporal chaos. When a limited number of observations is available, the reconstruction and identification of complex dynamical regimes become challenging problems. A method based on spatial recurrence properties is propos...

The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic windows can be easily made based on the maximum Lyapunov exponent of the system, this remains a challenging task for continuous systems, especially if only short ...