Thesis of Marrouane Ayyad

Defense of thesis Marrouane Ayyad - laboratory PhLAM

Abstract :

In Greek mythology, a chimera is a fantastic creature whose body parts belong to different animals.
By analogy with this mythology, in physics and more particularly in the study of spatially extended discrete complex systems, these chimera states correspond to the coexistence of two opposing spatio-temporal dynamic behaviors.
The coexistence of two domains, one coherent and the other incoherent in a chain of coupled non-linear oscillators is the historical example, like the different parts of the body of a chimera.
These spatio-temporal self-organizations have been widely studied theoretically and experimentally.
However, few studies have been carried out to explore the links between this type of dynamics and cellular automata.
These automata, despite their simplicity, have remarkable dynamic properties and, consequently, represent one of the foundations of information theory.

To answer this problem, we considered chimera states obtained in a chain of identical coupled optical resonators.
These structures were then the subject of quantitative and qualitative analyzes using the same tools as those used to characterize cellular automata.
This allowed us to highlight an elementary cellular automaton type dynamic hidden in the evolution of our chimera states.
We were then able to deduce a set of properties in terms of computability, opening perspectives towards potential applications for information processing.

Subsequently, we used our optical chimera states in the context of recurrent neural networks.
This is a new paradigm, which stands out for its great simplicity, speed and essential efficiency in the processing of information.
However, the performance of this machine learning technique depends in particular on the design of the reservoir.
Our results show that the implementation of our optical chimeric states instead of 'classic' reservoirs can provide a promising architectural alternative to further improve the speed of information processing.

Keywords : Chimera states,Spatiotemporal chaos,Nonlinear optics,Cellular automata,Reservoir computing,Self-organization