Nonlinear studies in the Institute of Cybernetics have been carried on since 1970's. In 80's the research was focused on Solid Mechanics, in 90's the research started to have another focal point - Nonlinear Dynamics. In this century the research has turned to new challenges - the complexity studies.
Characteristically, the attention has been shifted from problems of solid mechanics to interdisciplinary problems where stress field is one among the other fields. New qualities of nonlinear science like solitons, fractals, interaction waves, chaos, etc. should be taken into account. The basic continuum mechanics needed modification (nonlinearity, inhomogeneity, microstructure, internal variables, etc.), the methods of nonlinear dynamics have been widely used and improved, the mathematical modelling of complex processes in general have been motivated by physical analysis, the methods for numerical simulation derived with needed accuracy. In other words, around nonlinear dynamics, the various scientific disciplines emerge with their own specific aims but keeping the notion of nonlinearity and using the knowledge and often also methods of nonlinear dynamics. Our studies involve solids, fluids, biological tissues, signal processing, and differential equations.
So far CENS has focused on analytic research in natural complexity such as
- complexity in nonlinear wave motion, solitonics and coherent wave field, phase transformation fronts, thermodynamical constraints, anomalies of water waves
- complexity in biophysics: in silico modelling of cardiac contraction and cell energetics, internal variables
- fractality in nature: statistical topography, turbulent diffusion, heart rate variability
In addition, control and synthesis are now also in focus
- control systems
- proactive synthesis
The overviews on the research of the last decades are given in Annual Reports of Department of Mechanics (1991 ... 1998) and CENS (1999-2009).