Abstract: 

For over a century, many researchers have studied the dynamic changes in nonlinear dynamical systems because understanding transitions between regular, laminar and chaotic behaviors is essential to understanding the underlying mechanisms behind complex systems. Most studies were performed on the only available practical information, i.e. time series. In view of its ubiquity, studying time series is today an essential and challenging step to forecasting and detecting transitions. 
Studying transitions in low dimensional nonlinear dynamical systems is a complex problem for which there is not yet a simple and a global numerical method able to detect for examples chaotic-chaotic, chaotic-periodic, periodic-periodic bifurcations or symmetry-breaking and symmetry-increasing bifurcations. 
Sudden changes in complexity descriptors often reveal a deep modification of the operating mode of the system under study. Several complexity descriptors derived from different theories such as chaotic theory, geometric theory and information theory can be proposed as interesting alternatives. 
In this presentation I propose to review a certain number of existing measures of complexity and I complete it by presenting new complexity descriptors derived from the information theory through the concept of entropy (n-order fuzzy entropy, maximum similarity entropy), from the geometric theory through the concept of multifractal (coarse-grained multifractality analysis) and from the chaotic theory through the concept of recurrence (unbiased recurrence plots). 

Biography:Jean-Marc Girault received his master’s degree in signal processing and biological and medical imaging from the University of Angers, France, in 1996. He obtained his Ph.D. degree in signal processing in medical ultrasound imaging from the Francois Rabelais University of Tours, France, in 1999. Finally, he obtained his qualification for research supervision in signal processing in medical ultrasound imaging from the Francois-Rabelais University of Tours, in 2010. He has been a lecturer in signal processing at the University of Tours since 2001. His principle results achieved were in nonlinear signal analysis (complexity analysis with recurrence, entropies, symmetries, and multifractals) and processing (modeling and identification) and in ultrasound imaging. Most important findings were in optimal command (deterministic and stochastic) and blind deconvolution in ultrasound imaging, in sub-ultra-harmonics modeling and identification and in Doppler detectors and estimators (rhythm, velocity, and energy) applied for the studies involving microemboli and distressed foetus. He has written more than 90 scientific communications on medical ultrasound imaging and signal processing. Since 2005, he has been responsible for the master’s degree in medical imaging at the Francois-Rabelais University of Tours. At the same time, he coordinates the Signal-Imaging group in the team Imaging and Ultrasound in the research unit Imaging and Brain UMR U930, Tours, France