Understanding the emergence of patterns in natural (nonlinear) systems.
Understanding the emergence of natural patterns via a combination of nonlinear dynamics, ODE/PDE theory, functional analysis, inverse problems, numerical analysis and scientific computing. Qualitative and quantitative understanding of real-world systems ranging from biological systems, through medical applications to systems in earth science and physics.
The strategy of NDNS+ consists of three parts:
- Studying the mathematical principles underlying broad classes of dynamical systems, including coupled ODEs, PDEs, (random) maps, delay equations, networks, hybrid systems, etc.
- Developing computational, multi-scale analysis and dimension reduction techniques for the local and global analysis of large dynamical systems.
- Combining these fundamental insights and techniques with numerical simulation, observational data and machine learning, to predict, compute and shape the emergence of patterns in real-world systems, both qualitatively and quantitatively.