Efficient detection of periodic orbits in chaotic systems by stabilising transformations

Details Efficient detection of periodic orbits in chaotic systems by stabilising transformations Efficient detection of periodic orbits in chaotic systems by stabilising transformations

2005-02-07

arxiv.org/abs/nlin/0502013v2

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736] with a modified semi-implicit Euler iterative scheme and seeding with periodic orbits of neighbouring periods, has been shown to be highly efficient when applied to low-dimensional systems. The difficulty in applying the algorithm to higher-dimensional systems is mainly due to the fact that the number of the stabilising transformations grows extremely fast with increasing system dimension. Here we analyse the properties of stabilising transformations and propose an alternative approach for constructing a smaller set of transformations. The performance of the new approach is illustrated on the four-dimentional kicked double rotor map and the six-dimensional system of three coupled Henon maps.

Affiliated with

Also associated with

No associations

Rating

Efficient detection of periodic orbits in chaotic systems by stabilising transformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Efficient detection of periodic orbits in chaotic systems by stabilising transformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Efficient detection of periodic orbits in chaotic systems by stabilising transformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-129359