Topics of interest
PATTERN FORMATION, COMPETITION AND SPACE TIME CHAOS

 

CONTROL AND SYNCHRONIZATION OF CHAOTIC AND SPACE TIME CHAOTIC SYSTEMS





 

EXCITABLE MEDIA
 
PATTERN FORMATION, COMPETITION AND SPACE TIME CHAOS
see our Physics Reports for a review
Formation of patterns in extended systems out of the equilibrium is generally the result of the interplay between a local nonlinear dynamics and
gradient or nonlocal terms, coupling neighboring spatial regions. Patterning may emerge in various different circumstances. Their competition may
lead to intringuing phenomena, such as coexistence of space domains, or alternance of different symmetries, or even space time chaotic situations.
Recently, we have studied pattern formation and competition in nonlinear optical devices, as well as the formation and competition of
localized structures. For an overview on the current research lines see our pattern formation laboratory web page.
CONTROL AND SYNCHRONIZATION OF CHAOTIC AND SPACE TIME CHAOTIC SYSTEMS
Control of chaos refers to a process whereby a tiny perturbation applied to a chaotic system produces a desirable (chaotic, periodic or stationary)
behavior. Relevant issues connected with chaos control are targeting of chaos, and communicating with chaos, i.e. controlling chaotic motions carrying
desired symbolic sequences. An overview of the different problems and issues related with chaos control is available in our recent Physics Reports.
At variance, chaos synchronization describes a situation whereby a coupling between two (or many) chaotic units leads to the emergence of some
(synchronized) behavior among the different units. For a quite comprehensive overview, see our recent paper on synchronization, and References therein.
Interest is currently paid to study control and synchronization features in spatially extended systems, as well as to link these phenomena with pattern
formation, competition and space time chaos.
EXCITABLE MEDIA
Excitability is a dynamical property of some systems displaying a linearly stable stationary solution, that however can produce giant responses to an external
perturbation above a given threshold. Excitable behavior is an essential feature of some chemical reactions, and biophysical systems. In the past we have tried
to link this property to the fundamental features of bifurcations in the plane (click here to see an example). Our interest is now devoted to study the spatial
behavior of excitable media and to characterize the different phenomena that appear in coupled excitable units.