Recurrence plots and unstable periodic orbits.

Locating unstable periodic orbits in recurrence plots

Locating unstable periodic orbits in recurrence plots

Detecting unstable periodic orbits from transient chaotic time series

We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of f...

Recurrence plots for the analysis of complex systems

Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system’s behaviour in phase space.A powerful tool for their visualisation and analysis called recurrence plotwas introduced in the late 1980’s. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief...

Extracting dynamical structure from unstable periodic orbits.

The topological recurrence algorithm provides a fast and robust method for detecting the presence of unstable periodic orbits (UPO's) in short, noisy experimental data files. We present here a technique for improving this method by using a matrix fitting algorithm to extract dynamical information about the system from these UPO's. This method greatly increases the sensitivity of the algorithm, ...