Non-linear systems

Research into the mathematical treatment of systems which do not satisfy the principle of superposition (i.e. systems where the outputs are not directly proportional to the inputs). These often exhibit richly non-linear behaviour (e.g. 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.

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 (e.g. those around data science and urban living).

We will maintain this research area as a proportion of the EPSRC portfolio. This strategy aims to maintain the scale and quality of the research area within the EPSRC portfolio, while encouraging greater collaboration with other areas of the mathematical sciences and other disciplines. By the end of the Delivery Plan, we aim to have maintained a portfolio of Non-Linear Systems research and skills that:

  • Has strengthened 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 (Evidence source 1), 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 (e.g. network science)
  • Includes a cohort of early-career researchers (ECRs) who are comfortable working across disciplinary boundaries and able to take up positions of leadership in the community.

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 (Evidence source 2,3,4,5,6,7).

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 (Evidence source 2,3,4,5,6,7). 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 (Evidence source 4). 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 has increased significantly since the 2010 International Review of Mathematical Sciences (IRM), (Evidence source 6,7). There is some concern, however, regarding the continued supply of ECRs 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 (Evidence source 3).

This research area is relevant to all four Prosperity Outcomes in the long term, with its contribution  to the following Ambitions within Healthy and Connected Nation Outcomes prioritised:

H1: Transform community health and care

Use advanced analytical techniques to derive insight from complex datasets (e.g. those generated by pervasive sensor networks).

H2: Improve prevention and public health

Enable improved understanding of the spread of disease through advanced techniques for modelling complex transmission networks.

C1: Enable a competitive, data-driven economy

Use novel analytical approaches to complex data analytics to enable creative insights from data that can be applied across a range of sectors.

C2: Achieve transformational development and use of the Internet of Things

Use the development of advanced mathematical techniques to analyse and optimise devices interacting over a network.

Research area connections

This diagram shows the top 10 connections between Research Areas within the EPSRC research portfolio. The depth of the segment relates to value of grants and the width of the segment relates to the number of grants shared by those two Research Areas. Please click to see the related Research Area rationale.


We aim to maintain this area as a proportion of the EPSRC portfolio.

Visualising our Portfolio (VoP)
Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships.

EPSRC support by research area in non-linear systems (GoW)
Search EPSRC's research and training grants.

Contact Details

In the following table, contact information relevant to the page. The first column is for visual reference only. Data is in the right column.

Name: Michael Ward
Job title: Manager
Department: Mathematical Sciences
Organisation: EPSRC
Telephone: 01793 444196