Related papers: Controlling chaos in wave-particle interactions
We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in…
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for…
Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…
We describe a method of control of chaos that occurs in area-preserving maps. This method is based on small modifications of the original map by addition of a small control term. We apply this control technique to the standard map and to…
We propose a scheme for producing directed motion in a lattice system by applying a periodic driving potential. By controlling the dynamics by means of the effect known as coherent destruction of tunneling, we demonstrate a novel…
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…
It is demonstrated that improved entrainment control of chaotic systems can maintain periodic goal dynamics near unstable periodic orbits without feedback. The method is based on the optimization of goal trajectories and leads to small…
By sending many two-level atoms through a cavity resonant with the atomic transition, and letting the interaction times between the atoms and the cavity be randomly distributed, we end up with a predetermined Fock state of the…
We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above…
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…
A simple method to perform chaos control without the need of complex numerical and analytical calculations is proposed. The method works for dynamical systems with bounded solutions and in the trivial case of constant Jacobians.
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…
The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of…
We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a…
Recently, the Hamiltonian Control Theory was used in [Boreux et al.] to increase the dynamic aperture of a ring particle accelerator having a localized thin sextupole magnet. In this letter, these results are extended by proving that a…
The paper first discusses theoretically the off-resonance selective excitation method that is dependent on the atomic internal states and used to generate approximately a standard coherent state of harmonic oscillator. The coherent average…
We report experimental control of chaos in an electronic circuit at 43.9 MHz, which is the fastest chaos control reported in the literature to date. Limiter control is used to stabilize a periodic orbit in a tuned collector transistor…
Magnetic field line chaos occurs under the presence of non-axisymmetric perturbations of an axisymmetric equilibrium and is manifested by the destruction of smooth flux surfaces formed by the field lines. These perturbations also render the…
In recent years, there has been considerable interest in understanding the motion in Hamiltonian systems when phase space is divided into stochastic and integrable regions. This paper studies one aspect of this problem, namely, the motion…
Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with…