Detecting unstable periodic orbits in chaotic continuous-time dynamical systems.
We extend the recently developed method for detecting unstable periodic points of chaotic time-discrete dynamical systems to find unstable periodic orbits in time-continuous systems, given by a set of ordinary differential equations. This is achieved by the reduction of the continuous flow to a Poincaré map which is then searched for periodic points. The algorithm has global convergence properties and needs no a priori knowledge of the system. It works well for both dissipative and Hamiltonian dynamical systems which is demonstrated by exploring the Lorenz system and the hydrogen atom in a strong magnetic field. The advantages and general features of the approach are discussed in detail.
Pingel
D
D
Theoretical Chemistry, Institute for Physical Chemistry, Im Neuenheimer Feld 229, University of Heidelberg, Germany. detlef.pingel@tc.pci.uni-heidelberg.de
Schmelcher
P
P
Diakonos
F K
FK