Effects of time delayed position feedback on a van der Pol–Duffing oscillator

Xu, Jian; Chung, Kwok Wai

doi:10.1016/s0167-2789(03)00049-6

Cited by 182 publications

(99 citation statements)

References 35 publications

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“…Eventually, as can be seen in figure 14(b), after touching zero the stability boundary disintegrates and splits into separate stability regions. As any vibration will eventually die down in these regions, they are called amplitude death regions or death islands (see, for instance, Xu & Chung 2003). These regions are experimentally important for controlling the stability of the system.…”

Section: Viscous Dampingmentioning

confidence: 99%

“…Hence, the initial state space and the solution space of the delayed dynamical system are infinite dimensional. The theory of this type of equations lies in the area of functional differential equations discussed in details by Wu (1996), and some methods and results with applications to engineering problems can be found in Xu & Chung (2003).…”

Section: Introductionmentioning

confidence: 99%

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Real-time dynamic substructuring in a coupled oscillator–pendulum system

et al. 2006

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Real-time dynamic substructuring is a powerful testing method, which brings together analytical, numerical and experimental tools for the study of complex structures. It consists of replacing one part of the structure with a numerical model, which is connected to the remainder of the physical structure (the substructure) by a transfer system. In order to provide reliable results, this hybrid system must remain stable during the whole test. A primary mechanism for destabilization of these type of systems is the delays which are naturally present in the transfer system. In this paper, we apply the dynamic substructuring technique to a nonlinear system consisting of a pendulum attached to a mechanical oscillator. The oscillator is modelled numerically and the transfer system is an actuator. The system dynamics is governed by two coupled second-order neutral delay differential equations. We carry out local and global stability analyses of the system and identify the delay dependent stability boundaries for this type of system. We then perform a series of hybrid experimental tests for a pendulum–oscillator system. The results give excellent qualitative and quantitative agreement when compared to the analytical stability results.

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Section: Viscous Dampingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Real-time dynamic substructuring in a coupled oscillator–pendulum system

et al. 2006

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“…In recent times, considerable work has been carried out on the effect of time-delay in limit cycle oscillators [33,34], time-delay feedback [35,36], networks with time-delay coupling [37], etc. Recently, we have shown that even a single scalar delay equation with piecewise linear function can exhibit hyperchaotic behavior even for small values of time-delay [38].…”

Section: Introductionmentioning

confidence: 99%

Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems

Senthilkumar

Lakshmanan

2005

Phys. Rev. E

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The existence of anticipatory, complete and lag synchronization in a single system having two different time-delays, that is feedback delay τ 1 and coupling delay τ 2 , is identified. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay τ 2 with suitable stability condition is discussed. In particular, it is shown that the stability condition is independent of the delay times τ 1 and τ 2 . Consequently for a fixed set of parameters, all the three types of synchronizations can be realized. Further the emergence of exact anticipatory/complete/lag synchronization from the desynchronized state via approximate synchronization, when one of the system parameters (b 2 ) is varied, is characterized by the minimum of similarity function and the transition from on-off intermittency via periodic structure in laminar phase distribution.

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“…They focused on the bifurcation accompanying the change in number and stability of solutions. In [6], we studied a van der Pol-Duffing oscillator with time delayed position feedback and found two routes to chaos, namely period-doubling cascade and torus breaking.…”

Section: Introductionmentioning

confidence: 99%

Analysis of vibration suppression of master structure in nonlinear systems using nonlinear delayed absorber

Chen

Chung

et al. 2014

Int. J. Dynam. Control

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In this paper, a nonlinear delayed absorber is proposed by a delayed feedback loop and is utilized to absorb or suppress the vibration of a two-degree-of-freedom nonlinear system when the primary resonance and the 1:1 internal resonance occur simultaneously. To explain analytically mechanism of performance of the absorber, an integral equation method is provided to obtain the second order approximation and the amplitude equations. As a result, the feedback gain and time delay which make the amplitude of the main system equal to zero can be derived analytically. Optimal working conditions of the system are extracted from the time delay-response curves, the force-response curves and the frequency-response curves. In the illustrative example, the appropriate choice of feedback gains and time delays can reduce the amplitude of the main system by more than 98 % in comparison with the amplitude with no time delay. All analytical predictions are in excellent agreement with the numerical simulations.

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Effects of time delayed position feedback on a van der Pol–Duffing oscillator

Cited by 182 publications

References 35 publications

Real-time dynamic substructuring in a coupled oscillator–pendulum system

Real-time dynamic substructuring in a coupled oscillator–pendulum system

Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems

Analysis of vibration suppression of master structure in nonlinear systems using nonlinear delayed absorber

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