Related papers: Controlling chaos in area-preserving maps
We present a method to control transport in Hamiltonian systems. We provide an algorithm - based on a perturbation of the original Hamiltonian localized in phase space - to design small control terms that are able to create isolated…
In present paper we discuss the control of complex spatio-temporal dynamics in a {spatially extended} non-linear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A…
We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of…
We study topological conditions ensuring the presence of rotational chaos for non-wandering or area-preserving annular homeomorphisms. Compared to previous criteria, our main result provides a simpler alternative that avoids the need to…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
A method for the semiclassical quantization of chaotic maps is proposed, which is based on harmonic inversion. The power of the technique is demonstrated for the baker's map as a prototype example of a chaotic map.
We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic,…
Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small…
Rare events in non-linear dynamical systems are difficult to sample because of the sensitivity to perturbations of initial conditions and of complex landscapes in phase space. Here we discuss strategies to control these difficulties and…
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control…
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…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
In the positive column of a neon glow discharge, two different types of ionization waves occur simultaneously. The low-dimensional chaos arising from the nonlinear interaction between the two waves is controlled by a continuous feedback…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be…
We address the problem of applying Task and Motion Planning (TAMP) in real world environments. TAMP combines symbolic and geometric reasoning to produce sequential manipulation plans, typically specified as joint-space trajectories, which…