Area of investment and support

Area of investment and support: Non-linear systems

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).

Partners involved:
Engineering and Physical Sciences Research Council (EPSRC)

The scope and what we're doing

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.

Why we're doing it

UK research in non-linear systems is of very high quality with world leading researchers and centres based here. The community is therefore very well placed to contribute to the very many application areas.

Non-linear systems research is important to a wide array of other disciplines, both within the engineering and physical sciences and in other areas such as the life sciences and economic and social sciences.

More broadly, this research contributes to nearly all industrial sectors, a fact reflected in the strong role the area plays in the UK’s tradition of industrial mathematics. Indeed, a large majority of the EPSRC portfolio in this area is relevant to one or more industrial sectors.

Evidence from the Research Excellence Framework (REF) 2014 exercise suggests that overall researcher numbers working wholly or primarily within non-linear systems have increased significantly since the 2010 International Review of Mathematical Sciences (IRM). There is some concern, however, regarding the continued supply of early-career researchers as the first cohorts appointed in the area begin to reach the end of their careers and a significant cohort appointed in the 1990s and early 2000s reach more established career stages.

View evidence sources used to inform our research strategies.

Past projects, outcomes and impact

Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships. Find out more about research area connections and funding for non-linear systems.

Find previously funded projects on Grants on the Web.

Last updated: 3 January 2023

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