Syllabus
1) Hopf bifurcation (motivating examples, Hopf bifurcation theorem (approaches to proofs), numerical detection (test functions).
2) Steady state bifurcation of higher codimension (cusp, Takens-Bogdanov, Hopf-fold, Hopf-Hopf, Degenerate Hopf): Dynamical interpretation, normal forms, numerical detection.
3) Periodic solutions (Poincare map, stability of a periodic orbit, variational equation about a cycle). Bifurcation of periodic solutions (fold, period doubling, torus bifurcation).
4) Symmetry of dynamical systems (group of symmetries, symmetry breaking).
5) Non-smooth dynamical systens (examples). Filippov convex method. Classification of piecewise-smooth vector fields.
Annotation
Theory and numerical methods for bifurcation analysis.