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:
1. Studying the mathematical principles underlying broad classes of dynamical systems, including coupled ODEs, PDEs, (random) maps, delay equations, networks, hybrid systems, etc.
2. Developing computational, multi-scale analysis and dimension reduction techniques for the local and global analysis of large dynamical systems.
3. 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.