- Knowledge of phase portraits and how to sketch
- Knowledge of local bifurcations such as fold, transcritical, pitchfork and Hopf
- Knowledge of global bifurcations and homoclinic/heteroclinic connections
- Knowledge of dissipative systems and global attractors
- Awareness of applications of dynamical systems theory in physical/biological problems
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We introduce dynamical systems theory and examine how mathematics can be used to analyse qualitative changes in the system through bifurcations. This is now the cornerstone for many areas mathematical anaysis in biology, economics, finance, climate modelling and other physics etc as it can determine not only the long time dynamics but also the expected transients and how these change as parameters are varied. Hysteresis, where the path observed depends on the history, is an important example and can predicted using dynamical systems theory. We concentrate on continuous dynamical systems rather than maps. The course is intended as an introductory overview and builds on the ODE course WB104 (and so is primarily intended for second year students). We will examine dynamical systems, the basic forms of bifurcations and illustrate with some applications and hence introduces a number of other topics in applied mathematics.
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The course is intended as an introductory overview and builds on the ODE course WB104 (and so is primarily intended for second year students)
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Ordinary Differential Equations NWI-WB104
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