07/08/2017 - Where are we with the understanding of non-autonomous dynamics? - Palestrante: Aneta Stefanovska (Lancaster University-UK)

Seminário de Probabilidade e Sistemas Complexos

Palestrante: Aneta Stefanovska - Physics Department, Lancaster University, Lancaster, UK

Local: Auditorio Fernão (ICMC bloco 6)

Data e horário: 07 de Agosto de 2017 as 10:30

Título: Where are we with the understanding of non-autonomous dynamics?

Resumo: While chaotic dynamics attracted immense attention between mathematicians, physicists, life scientists, and in science quite generally in the last four decades, non-autonomous dynamics seems to have been brushed under the carpet. Yet, it is difficult to claim that chaotic behaviour has been observed in living systems, also because, to date, there is no reliable method for the detection of chaos from measured data. In contrast, there is ample evidence for the existence of time-varying non-autonomous dynamics. However, physicists especially consider non-autonomous dynamics as easy to deal with by transformation into autonomous dynamics, where there is an abundance of tractable analytic tools to tackle, or that it belongs to the class of stochastic systems where, again, numerous analytic approaches have been developed over the past few decades. In the talk, we will first present examples of non-autonomous dynamics measured from biological cells, the cardiovascular system and the brain, as well as from experiments with electrons on the surface of liquid helium, or rogue waves generation in water tanks.
Then, we will briefly review the existing numerical methods to detect and analyse non-autonomous dynamics from data. In the third part of the talk, we will summarise our current work on non-autonomous dynamics when the external perturbation is of quasi-periodic origin, arguing that most of the challenging problems still remain unsolved and that our better understanding of non-autonomous, finite-time dynamics could significantly advance our understanding of nature in general.