2 hrs lectures per week: Wednesday 13:15-15:00
week 6: UNNIK 101
week 7--16: UNNIK 103
week 18--21: BBG 109
The first lecture and
practicum are on February 10, 2016 (UNNIK 311, Heidelberglaan 2)
Presentation of individual examination problems is on June 22, 2016 at 14:00-17:00 (BBG 322/325)
|10 Feb 2016
||General ideas: Simulation,
continuation, and normal form analysis of ODEs and iterated
Multivariate Taylor formulas.
Newton method for systems of nonlinear equations.
Quadratic approximation of 1D invariant manifolds near equilibria.
|17 Feb 2016||Algebraic
continuation problems. Limit points.
Parameter, pseudo-arclength, and Moore-Penrose continuation methods.
Continuation of equilibria and fixed points.
|24 Feb 2016
points. Branch switching.
Detection and location of branching points.
|02 Mar 2016
technique - I. Detection of limit and branching points
|09 Mar 2016
product. Detection of Hopf bifurcation points.
Boundary-value continuation problems and their discretization via orthogonal collocation. Continuation of cycles.
Detection of limit points, period-doubling, and torus bifurcations of cycles.
|16 Mar 2016
||Review of codim 1
bifurcations of equilibria in n-dimensional ODEs.
Review of codim 1 local bifurcations of limit cycles in n-dimansional ODEs.
|23 Mar 2016
||Bordering technique - II. Continuation of fold and Hopf bifurcations of equilibria.||Practicum 7
|30 Mar 2016
||Continuation of fold, period-doubling, and torus bifurcations of limit cycles.||Practicum 8
|06 Apr 2016
||Computation of normal form coefficients for codim 1 bifurcations of equilibria.||Practicum 9
|13 Apr 2016
||Computation of periodic normal form coefficients for codim 1 bifurcations of limit cycles.||Practicum 10|
|20 Apr 2016
continuation of homoclinic orbits to hyperbolic equilibria
in n-dimensional ODEs.
|27 Apr 2016
||NO LECTURE||NO PRACTICUM|
|04 May 2016||Review of codim 1 bifurcations of fixed
points in n-dimensional maps.
Computation of normal form coefficients for codim 1 bifurcations of fixed points
|11 May 2016||Continuation of codim 1 bifurcations of fixed points. Detection of codim 2 bifurcations and branch switching.||Practicum 13|
|18 May 2016||Computation
1D invariant manifolds of saddle fixed points in
Continuation of homoclinic orbits to saddle fixed points in n-dimensional maps.
|25 May 2016
||Final remarks. Assignment of individual examination problems.||NO PRACTICUM|
|22 Jun 2016||Delivering of
written elaborations of the examination problems and their
oral presentation (14:00 -17:00, BBG 322/325)