Bifurcations are fascinating phenomena that can have a great impact on the stability and overall behavior of a system. They are often connected to system switches or tipping points, where system behavior can change drastically if environmental parameters cross some boundary value. The study of bifurcations in dynamical models of real-life systems is therefore of great importance to determine possible situations where catastrophic failure may occur.
This course looks at bifurcations occurring in dynamical systems from a mathematical viewpoint, but is aimed at Life Sciences students in the BIBC and other programmes.
At the end of the course, you should be able to:
- Analyse dynamical ODE models for the occurrence of bifurcations, and understand the model behavior around bifurcations.
- Identify various types of bifurcations and know their specific properties.
- Predict the behavior of models upon parameter changes.