Related papers: A simple method of chaos control
The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
A stochastic control of the vibrational motion for a single trapped ion/atom is proposed. It is based on the possibility to continously monitor the motion through a light field meter. The output from the measurement process should be then…
Aims. This paper investigates the chaotic rotation of an oblate satellite in the context of chaos control. Methods. A model of planar oscillations, described with the Beletskii equation, was investigated. The Hamiltonian formalism was…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject…
Structured decompositions of a desired unitary operator are employed to derive control schemes that achieve certain control objectives for finite-level quantum systems using only sequences of simple control pulses such as square waves with…
This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
A discrete-time method for solving problems in optimal quantum control is presented. Controlling the time discretized markovian dynamics of a quantum system can be reduced to a Markov-decision process. We demonstrate this method in this…
In this article we present an application of a method of control of Hamiltonian systems to the chaotic velocity diffusion of a cold electron beam interacting with electrostatic waves. We numerically show the efficiency and robustness of the…
The issue of white-noise-aided control is considered and its availability is proved. And a noise-aiding way is developed to stabilize perturbed systems to be input-to-state stable (ISS) with respect to (w.r.t.) perturbations. To illustrate…
We show the existence of a dynamical system without any distributionally scrambled pair which is semiconjugated to a distributionally chaotic factor.
The traditional approach to feedback control is to apply forces to a system by modifying the Hamiltonian. Here we show that quantum systems can be controlled without any Hamiltonian feedback, purely by exploiting the random quantum…
We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
In a dynamical systems description of spatiotemporally chaotic PDEs including those describing turbulence, chaos is viewed as a trajectory evolving within a network of non-chaotic, dynamically unstable, time-invariant solutions embedded in…