Aims and Scope

NDNS+ was created, in 2005, to address the inherent complexity of natural systems, and of the mathematical models that we use to describe them. The research of the cluster NDNS+ is organized in six themes:
  • Bifurcations and Chaos
  • Multiple Scales
  • Scientific Computing
  • Patterns and Waves
  • Variational Methods
  • Stochastic Dynamics
These are to be viewed as overlapping, where most people and most activities belong to several themes simultaneously. The research themes reflect the significant challenges that face us, and the opportunities that we now have to address these.

Some of the research themes of this programme are organized around tool sets for the analysis of differential equations. Bifurcation theory, Variational Methods and Scientific Computing are three complementary sets of tools for the analysis of differential equations, and we develop these three areas further to meet the specific demands of the complex systems that arise in the Earth and Life Sciences. In addition, the cluster provides a unique opportunity to bring these areas together and enhance their interaction.

The three other themes are oriented more towards phenomena than tools. A common element of complex systems in general, and specifically in those that arise in the natural environment, is their Multi-scale nature: behaviour that is well described at one scale is intrinsically dependent on behaviour at other (larger or smaller, faster or slower) scales. The understanding of Patterns and their evolution is central in the study of complex natural systems. Finally, the role of stochastic effects in otherwise deterministic models has strongly increased, and this reflected in the theme Stochastic Dynamics.

The cluster NDNS+ has been constructed around the interaction between mathematics on the one hand and the applications in the earth and life sciences on the other. Many of the cluster activities are inspired by questions arising from applications, and there are many close collaborations between cluster members and non-mathematicians.

Moreover, NDNS+ supports fundamental mathematical research on dynamical systems and related areas in analysis.

More detailed information about the research themes can be found in
this pdf