Applied nonlinear mathematics
Mathematical models of real-world phenomena are often nonlinear and too complicated to be solved exactly. Thus, new mathematical methods are required to analyse these models and determine what their solutions say about the real-world situation they are meant to describe.
The Engineering Mathematics Research Group has a world-leading legacy of developing tools that can be applied to nonlinear mathematical models. By using these tools to understand the solutions of nonlinear models, new insights can be made into real-world processes arising in fields such as biology, physics, engineering, and industry. For example, the solutions to nonlinear mathematical models can help to explain how the stripes on a zebra form or why birds flock together in the sky.
Our research focuses on topics such as:
- Smooth and non-smooth dynamical systems
- Bifurcation and catastrophe theory
- Asymptotic methods
- Collective dynamics
Applications of our research include:
- Pattern formation in biology
- Contact and friction
- Spreading of viruses
- Energy harvesting
- Pedestrian motion
Associated group members:
- David Barton
- Alan Champneys
- Oscar Benjamin
- Yani Berdeni
- Nikolai Bode
- John Hogan
- Mike Jeffrey
- Anthony Mulholland
- Helena Stage
- Robert Szalai