Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control
نویسندگان
چکیده
منابع مشابه
Stabilizing unstable periodic orbits with delayed feedback control in act-and-wait fashion
A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off alternately at every integer multiples of the period of the system. By analyzing the monodromymatrix of the closed-loop system, we obtain conditions under whi...
متن کاملUnstable periodic orbits in the Lorenz attractor.
We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computatio...
متن کاملStabilizing the unstable periodic orbits of a chaotic system using model independent adaptive time-delayed controller
In this paper we deal with the control of chaotic systems. Knowing that a chaotic attractor contains a myriad of unstable periodic orbits (UPO’s), the aim of our work is to stabilize some of the UPO’s embedded in the chaotic attractor and which have interesting characteristics. First, using the input-tostate linearization method in conjunction with a timedelayed state feedback, we design a cont...
متن کاملStabilization of unstable steady states and periodic orbits in an electrochemical system using delayed-feedback control.
We report numerical and experimental results indicating successful stabilization of unstable steady states and periodic orbits in an electrochemical system. Applying a continuous delayed-feedback technique not only periodic and chaotic oscillations are suppressed via stabilization of steady-state solutions but also the chaotic dynamics can be converted to periodic behavior. In all cases the fee...
متن کاملUnstable periodic orbits and Attractor of the Lorenz Model
Numerical method for detection of unstable periodic orbits on attractors of nonlinear dynamical systems is proposed. This method requires the similar techniques as the data assimilation does. This fact facilitates its implementation for geophysical models. Some low-period orbits of the Lorenz model have been calculated explicitely. The orbits encoding and application of symbolic dynamics is use...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2007
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.76.056214