相关论文: Controlling Chaos using an Exponential Control
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…
Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed…
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…
We report on a significant improvement of the classical time-delayed feedback control method for stabilization of unstable periodic orbits or steady states. In an electronic circuit experiment we were able to realize time-varying and…
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…
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…
We generalize a method of control of chaos which uses delayed feedback at the period of an unstable orbit to stabilize that orbit. The generalization consists of substituting some portion of the nonlinear dynamical system with a delayed…
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…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
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…
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…
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…
This paper is devoted to the stabilization problem for nonlinear driftless control systems by means of a time-varying feedback control. It is assumed that the vector fields of the system together with their first order Lie brackets span the…
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…
Analysis of the PPF chaos control method used in biological experiments shows that it can robustly control a wider class of systems than previously believed, including those without stable manifolds. This can be exploited to find the…
Chaotic behavior can be produced from difference equations with unstable fixed points. Difference equations can be used for algorithms to control the chaotic behavior by perturbing a system parameter using feedback based on the first…
The Pyragas method for controlling chaos is investigated in detail from the experimental as well as theoretical point of view. We show by an analytical stability analysis that the revolution around an unstable periodic orbit governs the…
A class of nonlinear control-affine systems with bounded time-varying drift is considered. It is assumed that the control vector fields together with their iterated Lie brackets satisfy Hormander's condition in a neighborhood of the origin.…