Nonlinear time series analysis of stochastic and dynamical complex systems

Nonlinear time series analysis of stochastic and dynamical complex systems

Most systems in nature are neither completely ordered nor completely disordered, but something in between. Complexity is characterized by a certain degree of organization and patterns. Within the framework of Information Theory, the statistical complexity of a system is zero in the extreme situations of complete knowledge (or “perfect order”) and total ignorance (or “complete randomness”). Both are simple situations, as one is fully predictable, and the other one has a simple statistical description. In order to capture the diversity and the rich spectrum of unpredictability occurring between these two extreme situations, many statistical complexity measures have been proposed in the literature, which are useful tools for analyzing high-dimensional and stochastic dynamical systems presenting underlying, hidden, or unobserved states that might organize the system’s behavior.

Recent presentations:

Distinguishing signatures of determinism and stochasticity in spiking complex systems (XXXIII Dynamics Days Europe, Madrid, Spain, June 2013)

Introduction to symbolic time series analysis applied to climatological data (Second LINC School, Soesterberg, The Netherlands, April 2013)

Funding: Institució Catalana de Recerca I Estudis Avançats (ICREA) through the ACADEMIA AWARD 2009, the European Office of Aerospace Research & Development (EOARD) through grant FA8655-12-1-2140 (2012-2013), and the Marie Curie Initial Training Network LINC.