Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of di ....Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of disease.Read moreRead less
Complex dynamical systems: inferring form and function of interacting biological systems. Often in biology a large number of simple parts interacting according to simple rules can result in behaviour that is rich and varied. This project aims to develop the mathematics of complex systems theory to describe how such collections of simple interacting parts can form large complicated structures, and to deduce what dynamical behaviour can result.
Quantifying complexity and measuring structure within complex systems. Most interesting systems are complex. The complex systems of interest in this project are characterised by a simple dynamical behaviour on each individual part; and a complicated web of interaction between the many distinct parts. The project will focus on the massive system of interacting neurones in the brain, and transmission of influenza via interpersonal contacts. This project will provide a better model of that web of i ....Quantifying complexity and measuring structure within complex systems. Most interesting systems are complex. The complex systems of interest in this project are characterised by a simple dynamical behaviour on each individual part; and a complicated web of interaction between the many distinct parts. The project will focus on the massive system of interacting neurones in the brain, and transmission of influenza via interpersonal contacts. This project will provide a better model of that web of interactions; and new methods for statistically validating this model against data. Existing models of complex networks are statistically biased so, by employing robust statistical methodologies, this problem will be rectified and provide a method for randomly choosing representative complex systems. Read moreRead less
Improving transient performance for systems with multiple inputs/outputs. This project aims to develop and test new mathematical techniques for the improvement of transient performance in tracking control systems. The fundamental problem to be addressed will be the design of controllers to rapidly track constant and time varying target reference signals without overshooting or undershooting for multiple-input multiple-output systems/plants. These new methods aim to offer improved accuracy and sp ....Improving transient performance for systems with multiple inputs/outputs. This project aims to develop and test new mathematical techniques for the improvement of transient performance in tracking control systems. The fundamental problem to be addressed will be the design of controllers to rapidly track constant and time varying target reference signals without overshooting or undershooting for multiple-input multiple-output systems/plants. These new methods aim to offer improved accuracy and speed in many engineering applications.Read moreRead less