Related papers: A simple method of chaos control

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…

The main purpose of this paper is to present a general method for the controllability of the stability of a system of fractional-order differential equations around its equilibrium states. This method is applied to analyze and control the…

We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…

We present a method of control of chaos in area-preserving maps. This method gives an explicit expression of a control term which is added to a given area-preserving map. The resulting controlled map which is a small and suitable…

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…

This paper deals whith the stabilization of any UPO of a chaotic map by modulation of a control parameter. It concentrates on proportional and delayed feedback control methods. Alternative types of these methods are proposed and their…

This paper presents an optimal dynamic control framework for bounded Jacobian nonlinear discrete-time (DT) systems with nonlinear observations affected by both state and process noise. Rather than directly stabilizing the uncertain system,…

We consider the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence, via the application of a control Hamiltonian, without any additional resources. In this case neither quantum error…

One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…

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…

This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…

We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…

The spatiotemporal chaos in the Frenkel-Kontorova (FK) model is studied. A model-free reinforcement learning algorithm is proposed to the design of a controller. There is no need for explicit knowledge on system, target states and unstable…

In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0 < \alpha <2$. The method is tested on various forms of fractional generalizations of the…

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative, oscillator systems by weak harmonic excitations is presented, including diverse applications…

Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…

We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…

If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…

We consider a mixed chaotic Hamiltonian system and compare classical with quantum chaos. As alternative to the methods of enegy level spacing statistics and trace formulas, we construct a quantum action and a quantum analogue phase space to…