Many engineering systems can be characterised as complex since they have a nonlinear behaviour incorporating a stochastic uncertainty. Urban traffic systems or traffic pollution propagation models are typical representatives of such complex systems. One of the most appropriate methods for modelling such systems is based on the application of Gaussian processes.

The aim of the project is to develop several aspects of the theory of Gibbs states and phase transitions of lattice models. Gradient lattice models, where the challenge is to understand the case of non-convex potentials, will be studied by means of multiscale analysis and a refinement of cluster expansions.

The project is aimed at nonlinear dynamics application to monetary and financial economics. The area aof monetary research will be aimed at classical macro monetary nonlinear models, where the potentials of complex dynamics (chaos) will be investigated. Analysis of the model of real business cycles and models of dynamic equilibrium will be also addressed by the project.