Related papers: Viewing the efficiency of chaos control
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…
We present the control of the high-dimensional chaos, with possibly a large number of positive Lyapunov-exponents, of unknown time-delay systems to an arbitrary goal dynamics. We give an existence-and-uniqueness theorem for the control…
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…
The presence of a nonattractive chaotic set, also called chaotic saddle, in phase space implies the appearance of a finite time kind of chaos that is known as transient chaos. For a given dynamical system in a certain region of phase space…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating…
We present a technique to control chaos in Hamiltonian systems which are close to integrable. By adding a small and simple control term to the perturbation, the system becomes more regular than the original one. We apply this technique to a…
In this work, we demonstrate the open-loop control of chaotic systems by means of optimized periodic signals. The use of such signals enables us to reduce control power significantly in comparison to simple harmonic perturbations. It is…
One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a…
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability,…
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…
The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi and York (OGY method) to stabilize the motion of a spacecraft around the triangular…
The dynamics of activation waves in excitable media can give rise to spiral turbulence, the resulting spatiotemporal chaos being associated with empirical biological phenomena such as life-threatening disturbances in the natural rhythm of…
Partial control is a technique used in systems with transient chaos. The aim of this control method is to avoid the escape of the orbits from a region Q of the phase space where the transient chaotic dynamics takes place. This technique is…
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…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…