Graduate (MAGIC) course Dynamical Systems: Flows

By Alastair Rucklidge
Graduate (MAGIC) course Dynamical Systems: Flows
These are lecture notes (slides) for a 10-hour course delivered as part of the MAGIC suite of graduate-level courses in nonlinear dynamics and dynamical systems. The course was all about flows; there is a follow-on course on maps and another on equivariant bifurcation theory.

Topics covered (in 9 lectures) were:

Flows and the Poincare map; Linearisation; Stability of equilibrium points, periodic orbits and other invariant sets; Local and global bifurcation theory; Centre Manifold Theorem; Birkhoff normal form; Local bifurcations of periodic orbits; An in-depth example (the saddle-node--Hopf bifurcation); Homoclinic bifurcations.

There was then an option in the last lecture for students to hear about PDEs, patterns, and the role of symmetry (leading in to a further 10 lectures on equivariant bifurcation theory by Pete Ashwin, or on hydrodynamic stability theory), or Numerical methods for dynamical systems (Symbolic algebra, Integrating ODEs and Continuation).
Author Institutional Affiliation
Alastair Rucklidge
University of Leeds
Tutorial LevelAdvanced Tutorial
Contest EntryYes

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