The numerical computation of connecting orbits in dynamical systems. (English) Zbl 0706.65080

Beyn, W.-J.

IMA J. Numer. Anal. 10, No. 3, 379-405 (1990).

Structural changes in dynamical systems are often related to the appearance or disappearance of orbits connecting two stationary points. A direct numerical method for the computation of connecting orbits and their associated parameter values is developed. The author employs a general phase condition and truncates the boundary-value problem to a finite interval by using on both ends the technique of asymptotic boundary conditions. The approximation error caused by this truncation is shown to decay exponentially.

Reviewer: E.Eitelberg

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
37-XX	Dynamical systems and ergodic theory

Keywords:

iterative method; dynamical systems; stationary points; connecting orbits; phase condition; asymptotic boundary conditions

Software:

AUTO; PASVA3