Research into the mathematical treatment of systems which do not satisfy the principle of superposition (in other words, systems where the outputs are not directly proportional to the inputs).
Non-linear systems encompasses research into the mathematical treatment of systems which do not satisfy the principle of superposition (systems where the outputs are not directly proportional to the inputs). These often exhibit richly non-linear behaviour (for example bifurcations, discontinuities and chaos) and are found throughout engineering, the physical sciences, the life sciences and the economic and social sciences.
The mathematical foundations of non-linear systems are drawn from dynamical systems, a branch of global analysis overlapping strongly with the mathematical analysis research area. Research in this area may incorporate aspects of complexity science.
The quality of UK research and training in this area is very high. The area is of considerable importance to a wide variety of other disciplines, application areas and industrial sectors. Non-linear systems research also contributes important theoretical foundations to key research challenges (for example those around data science and urban living).
This strategy aims to maintain the quality of the research area within the EPSRC portfolio, while encouraging greater collaboration with other areas of the mathematical sciences and other disciplines.
We aim to maintain a portfolio of non-linear systems research and skills that:
- strengthens links with other relevant disciplines, including engineering and information and communications technologies (ICT), as well as application areas, drawing on mathematical sciences infrastructure to facilitate the development of new connections
- builds on these connections to contribute to EPSRC prosperity outcomes and complement the Alan Turing Institute’s key capabilities, especially mathematical representations and inference and learning
- is well connected with other areas of the mathematical sciences, especially mathematical analysis, mathematical biology, and geometry and topology
- supports fundamental research into mathematical tools and techniques relevant to complexity science (for example, network science)
- includes a cohort of early-career researchers who are comfortable working across disciplinary boundaries and able to take up positions of leadership in the community.