Detecting unstable periodic orbits in switched arrival systems
نویسنده
چکیده
In this paper, a chaotic switched arrival system is considered. Poincaré section and Poincaré mapping are introduced for defining periodic orbits of this hybrid system. We propose a time-delayed impulsive feedback method to detect unstable periodic orbits embedded in the chaotic attractor. The convergence of the proposed algorithm is proved.
منابع مشابه
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 propert...
متن کاملDetecting unstable periodic orbits in high-dimensional chaotic systems from time series: reconstruction meeting with adaptation.
Detecting unstable periodic orbits (UPOs) in chaotic systems based solely on time series is a fundamental but extremely challenging problem in nonlinear dynamics. Previous approaches were applicable but mostly for low-dimensional chaotic systems. We develop a framework, integrating approximation theory of neural networks and adaptive synchronization, to address the problem of time-series-based ...
متن کاملEfficient algorithm for detecting unstable periodic orbits in chaotic systems.
We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of an iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect ...
متن کاملDetecting Unstable Periodic Orbits in Hyperchaotic Systems Using Subspace Fixed-Point Iteration
We present a numerical method for efficiently detecting unstable periodic orbits (UPO's) embedded in chaotic attractors of high-dimensional systems. This method, which we refer to as subspace fixed-point iteration, locates fixed points of Poincaré maps using a form of fixed-point iteration that splits the phase space into appropriate subspaces. In this paper, among a number of possible implemen...
متن کاملDetecting 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...
متن کامل