Point-to-periodic and periodic-to-periodic connections
In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, "On well-posed problems for connecting orbits in dynamical systems", where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms.
Connecting orbits, Continuation of invariant subspaces, Monodromy matrix, Periodic orbits, Projection boundary conditions
Dieci, Luca, and Jorge Rebaza. "Point-to-periodic and periodic-to-periodic connections." BIT numerical mathematics 44, no. 1 (2004): 41-62.
BIT Numerical Mathematics