Refuting the Odd-Number Limitation of Time-Delayed Feedback Control
نویسندگان
چکیده
منابع مشابه
Refuting the odd-number limitation of time-delayed feedback control.
We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation, which has a single real unstable Floquet multipli...
متن کاملOdd Number Limitation in Delayed Feedback Control
This chapter reviews the so-called odd number limitation in delayed feedback control (DFC) for chaotic systems. By the odd number limitation, the original DFC restricts the application to a special class of chaotic systems. So far, various methods have been developed to overcome the limitation. In this chapter, we show their key concepts to solve the problem.
متن کاملBeyond the odd number limitation: a bifurcation analysis of time-delayed feedback control.
We investigate the normal form of a subcritical Hopf bifurcation subjected to time-delayed feedback control. Bifurcation diagrams which cover time-dependent states as well are obtained by analytical means. The computations show that unstable limit cycles with an odd number of positive Floquet exponents can be stabilized by time-delayed feedback control, contrary to incorrect claims in the liter...
متن کاملTowards easier realization of time-delayed feedback control of odd-number orbits.
We develop generalized time-delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive Floquet exponents, which are particularly well suited for experimental realization. We construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods. In particular, it is shown how periodic orbits can ...
متن کاملLimitation of Generalized Delayed Feedback Control for Discrete-time Systems
In this paper, the stabilizability problem for chaotic discrete-time systems under the generalized delayed feedback control (GDFC) is addressed. It is proved that 0 < det(I − A) < 2 is a necessary and sufficient condition of stabilizability via m-step GDFC for an n-order system with Jacobi A. The condition reveals the limitation of GDFC more exactly than the odd number limitation. An analytical...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2007
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.98.114101