# Mathematical Basis of Tipping Points

Finding the mathematical basis of 'tipping points' through bifurcation analysis will help us discover whether or not accurate mathematical representations of physical or socioecomic systems display tipping point behaviour. In mathematics, a bifurcation is a point at which small changes start to grow rapidly, through positive feedbacks. If the systems studied do behave like bifurcations then it may be possible to predict 'tipping points' we encounter in the world. In chaos theory, a well-known example of a system that bifurcates is a Lorenz attractor originally derived from a model of convection in the earth's atmosphere. Studying how different kinds of systems bifurcate will help researchers determine whether or not a particular system could 'tip'.

This work package will use data provided from WP1 and WP2 to develop mathematical representations that describe the system behaviour of each. It will address the characteristics of the equations themselves, using techniques central to non-linear dynamical systems analysis and will use Bayesian methods to explore how the precursors to change can be identified in pre-change system states and also assess the ways in which the uncertainties that arise from system state impact mathematical models.

## Researchers

**Leaders:** Professors Michael Goldstein (Mathematical Sciences) and Brian Straughan (Mathematical Sciences)

**Research Associates: **Dr Camila Caiado (Mathematical Sciences) and Dr John Bissell (Mathematical Sciences)

**Additional Researchers:** Dr James Blowey, Dr Djoko Wirosoetisno and Dr Max Jensen (Mathematical Sciences), one leader each from WPs 1, 2 and 4