Aim and vision – University of Copenhagen

Dynamical Systems > Aim and vision

The project - Aim and vision

A long standing challenge in complex systems is how to understand the interaction between large numbers of constituents, for the purpose of understanding their macroscopic nature. The overall aim of the Dynamical Systems Interdisciplinary Network is to develop mathematical models and statistical methods suited for the analysis of empirical data obtained from such systems.

The aim is to better understand the dynamics, regulatory properties as well as how the dynamics are affected by random perturbations.

The statistical methodology will enable analysis of high-dimensional systems, and in particular, discover simple structures in complex data. Such insight is essential for prediction of future behaviour and for understanding flux regulation, oscillations, bifurcations, synchronization, chaos, and uniquely for this proposal, metastable non-equilibrium states.

A major challenge is to extract information from huge data sets produced in modern quantitative sciences, on how measurable components work together as a dynamical system - to achieve an understanding beyond that obtained by studying isolated components. For this it is essential to combine a deep knowledge of the subject matter with statistical and mathematical insight.

The theoretical research will focus on issues of central importance to applications, which in turn will serve as a testing ground for new methodology. The project will facilitate the flow of ideas between research areas that share similar methodological challenges but where collaboration is uncommon.

Common challenges for scientists across disciplines

Different complex systems often have common attributes and therefore pose common challenges for scientists across disciplines. Some of the attributes are:

  • strong degree of hierarchical organization,
  • constituents of a sub-system on one scale has much more interaction within the sub-system than across subsystems,
  • qualitative aspects of behaviors are repeated over time, but are quantitatively difficult to characterize,
  • feedback mechanisms are pervasive, and 
  • stability is dominant in spite of flexibility and the large behavioral repertoire.

A field rich in examples of such complex systems is biology. For instance, a neuron contains a complex biochemical interaction as well as morphology. Spines, dendrites and shafts are all small constituents of a neuron. Each neuron is a constituent in a local network. Each local network is a constituent in a large-scale brain structure, and each brain area is a constituent of the brain. The vascular blood flow in the kidneys, metabolic pathways, protein dynamics, psychological processes and economic behaviors have similar features.

The link between the individual elements and the macroscopic function is by no means obvious, and describing and understanding parallel processes in general is the key in these systems.