相关论文: Equivariant Versions of Odd Number Theorem
Equivariant Pyragas control is a delayed feedback method that aims to stabilize spatio-temporal patterns in systems with symmetries. In this article, we apply equivariant Pyragas control to discrete waves, which are periodic solutions that…
The Pyragas method of feedback control has attracted much interest as a method of stabilising unstable periodic orbits in a number of situations. We show that a time-delayed feedback control similar to the Pyragas method can be used to…
In the spirit of the well-known odd-number limitation, we study failure of Pyragas control of periodic orbits and equilibria. Addressing the periodic orbits first, we derive a fundamental observation on the invariance of the geometric…
We present an algorithm for a time-delayed feedback control design to stabilize periodic orbits with an odd number of positive Floquet exponents in autonomous systems. Due to the so-called odd number theorem such orbits have been considered…
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…
Pyragas time delayed feedback control has proven itself as an effective tool to non-invasively stabilize periodic solutions. In a number of publications, this method was adapted to equivariant settings and applied to stabilize branches of…
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…
We propose a necessary condition for the successful stabilisation of a periodic orbit using the extended version of time-delayed feedback control. This condition depends on the number of real Floquet multipliers larger than unity and is…
In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target…
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…
Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form…
We show that Pyragas delayed feedback control can stabilize an unstable periodic orbit (UPO) that arises from a generic subcritical Hopf bifurcation of a stable equilibrium in an n-dimensional dynamical system. This extends results of…
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…
We prove an analytical limitation on the use of time-delayed feedback control for the stabilization of periodic orbits in autonomous systems. This limitation depends on the number of real Floquet multipliers larger than unity, and is…
We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular non-invasive control schemes, such as…
The problem of stabilization of unstable periodic orbits of discrete nonlinear systems is considered in the article. A new generalization of the delayed feedback, which solves the stabilization problem, is proposed. The feedback is…
Irregular, especially chaotic, behavior is often undesirable for economic processes because it presents challenges for predicting their dynamics. In this situation, control of such a process by its mathematical model can be used to suppress…
For many years it was believed that an unstable periodic orbit with an odd number of real Floquet multipliers greater than unity cannot be stabilized by the time-delayed feedback control mechanism of Pyragus. A recent paper by Fiedler et al…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…
The OGY method is one of control methods for a chaotic system. In the method, we have to calculate a stabilizing periodic orbit embedded in its chaotic attractor. Thus, we cannot use this method in the case where a precise mathematical…