Dynamical Systems

Dynamical Systems Synopsis

The investigation of special topics in systems dynamics -uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory-has become a major issue at the System and Decision Sciences Research Program of the International Insti- tute for Applied Systems Analysis. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under vari- ations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of non- linear dynamic systems theory to biomathematics and ecoloey.