TY  - JOUR
AB  - It is known that branches of homoclinic orbits emanate from a singular point of a dynamical system with a double zero eigenvalue (Takens-Bogdanov point). We develop a robust numerical method for starting the computation of homoclinic branches near such a point. It is shown that this starting procedure relates to branch switching. In particular, for a certain transformed problem the homoclinic predictor is guaranteed to converge to the true orbit under a Newton iteration.
DA  - 1994
DO  - 10.1093/imanum/14.3.381
KW  - homoclinic orbits
KW  - Takens-Bogdanov points
KW  - singular stationary points
KW  - dynamical systems
KW  - center manifold reduction
LA  - eng
IS  - 3
M2  - 381
PY  - 1994
SN  - 0272-4979
SP  - 381-410
T2  - IMA Journal of Numerical Analysis
TI  - Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17842489
Y2  - 2024-12-27T02:12:35
ER  -