TY  - JOUR
AB  - Structural changes in dynamical systems are often related to the appearance or disappearance of orbits connecting two stationary points (either heteroclinic or homoclinic). Homoclinic orbits typically arise in one-parameter problems when on a branch of periodic solutions the periods tend to infinity (e.g. Guckenheimer & Holmes, 1983). We develop a direct numerical method for the computation of connecting orbits and their associated parameter values. We employ a general phase condition and truncate the boundary-value problem to a finite interval by using on both ends the technique of asymptotic boundary conditions; see, for example, de Hoog & Weiss (1980), Lentini & Keller (1980). The approximation error caused by this truncation is shown to decay exponentially. Based on this analysis and additional numerical investigations we set up an adaptive strategy for choosing the truncation interval.
DA  - 1990
DO  - 10.1093/imanum/10.3.379
KW  - phase condition
KW  - connecting orbits
KW  - stationary points
KW  - iterative method
KW  - dynamical systems
LA  - eng
IS  - 3
M2  - 379
PY  - 1990
SN  - 0272-4979
SP  - 379-405
T2  - IMA Journal of Numerical Analysis
TI  - The numerical computation of connecting orbits in dynamical systems
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17842543
Y2  - 2024-11-22T03:06:03
ER  -