Detecting unstable periodic orbits in chaotic continuous-time dynamical systems - art. no. 026214

摘要

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 Poincare 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. [References: 43]