Section for Dynamical Systems

The section performs research within a broad range of areas within dynamical systems – from energy systems to aerodynamics –  including modelling, forecasting, optimization, and controlling in both deterministic and stochastic systems. 

Dynamical Systems
Dynamical Systems section October 2023

We use dynamical systems mathematics to describe everything from chemical reactions and signal patterns in the human nervous system, robot movements and energy systems, the kinematics of planetary systems and the workings of smart cities.

By applying dynamical systems mathematics, you may reduce the amount of equations to solve large and extremely complex practical problems in these areas. We utilise advanced mathematical techniques to reduce the number of computations to a manageable level. This allows us to obtain a better understanding of highly detailed structures.

The mission of the section is to conduct research on all levels around dynamical systems. This involves both deterministic and stochastic systems, discrete and continuous systems, deductive and inductive model building, forecasting, and descriptions, as well as control and optimization.

The research at the Dynamical Systems Section is very wide ranging. From foundational research in work on statistical forecasting, modeling of spatial and temporal processes and time series analysis to applied research in wind- and solar power forecasting, electricity price forecasting and in the modelling and forecasting of district heating system.

Research areas

Renewable Energy and Sustainability

Development of time series and statistical methods as central computational tools for the transition from fossil energy to renewable energy and sustainable use of resources in general. A sizeable fraction of the research is based on specific problems in the energy sector, which is reflected in intensive collaboration with various industrial companies and in interdisciplinary projects.

Forecasting methodologies are central for decision making in energy consumption and production from fluctuating renewable energy sources such as wind, solar and hydro power. This includes electric price forecasting for regulating desirable consumer behaviour. Advances pertain to analysis of data using space and time hierarchies and obtaining coherence of data by online reconciliation procedures.

Mathematical methods for optimal control of district heating systems require advanced nonlinear models of the network dynamics for control purposes. The same holds for the dynamics of the electric power grid. Core research in optimization and control plays a central role in using digital solutions for the green transition.

Mathematical Biology

A number of disciplines in biology and health care use mathematical modelling for supporting the development of medicine, predicting infectious disease spreading, studying evolution of ocean habitats and in general gain scientific insight into biological systems.

Game theoretical approaches and stochastic methods are used to investigate the vertical daily migration patterns of marine life. Evolution of microorganisms and fish species is modelled by stochastic differential equation and diffusion advection equations. Models provide insight into evolution of marine populations relevant for the fishing industry.

Bacterial growth patterns are likewise investigated using diffusion-reaction-advection equations in cooperation with experimentalists. Focus is on the influence of antibiotics and probiotics. Biochemical networks and systems biology is a research topic covering numerous biological phenomena. Methods applied include statistics and big data approaches.

Disease spreading as for covid’19 is investigated by extended SIR-type models, where SIR stand for Susceptible, Infectious and Recovery. The extensions pertain to various segmentations based on e.g. geography, age, occupation, and others. Time delay in transmitting disease using integro-differential equations is another example of extended SIR type models being studied.