The research activities currently conducted in the Center cover a broad spectrum of natural sciences. They are tightly connected by the unity of the underlying concepts and methods.
A first type of activity deals with the manifestations of nonlinear dynamics and chaos at the macroscopic level. The mathematical and physico-chemical prerequisites for the onset of complex behavior are explored, and tools for the classification, characterization and quantitative description of the resulting regimes are elaborated. Of special interest is the propensity of systems driven away from equilibrium, by fluxes of matter and/or energy, to exhibit self-organized spatio-temporal behavior. Mathematical models for these phenomena are being developed for reaction-diffusion systems, fluids and interfaces, irradiated materials and driven systems undergoing phase transitions.
A second type of activity addresses the connection between dynamics at the microscopic and mesoscopic levels and complexity at the macroscopic level. The topics involved are interlinked by the use of probabilistic concepts. A major question explored pertains to the role of microscopic chaos in quantum dynamics, in classical transport phenomena and in the structure of nonequilibrium states. The conditions for a clearcut separation between macroscopic behavior, as described e.g. by the equations of fluid dynamics or chemical kinetics, and dynamical processes at the microscopic level are also analyzed. In particular, a detailed study of the fluctuations - the spontaneous deviations of the state variables from their macroscopic values - is carried out with emphasis on low-dimensional systems. In parallel, numerical simulation methods especially designed for the study of nonequilibrium systems are being developed. They constitute for the theoretician an ideal "laboratory" allowing him to test conjectures and to explore regimes inaccessible to existing theories or even to traditional experimental techniques.
The third type of activity extends beyond the strict realm of physical sciences. It addresses problems related to evolutionary and organizational processes in multi-unit systems. Such systems seem to have been selected in the natural world for information-processing purposes, owing to their ability to exhibit high plasticity in their reactions to external stimuli. Nonlinear dynamics underlies a variety of phenomena in such complex systems, from the regulation of the immune system to the collective processes in animal societies as well as in artificial systems. The possibility of applications of nonlinear science in technology - oriented problems is also being explored.