Analysis of a ring of mutually coupled van der Pol oscillators with coupling delay

Kouda, A.; Mori, Shohei

doi:10.1109/tcs.1981.1084964

Cited by 11 publications

(11 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This coupling is not necessarily instantaneous and might exhibit propagation delays which are comparable to or larger than the characteristic oscillatory time scale of the individual oscillators. The influence of such a latency in the coupling has already been addressed for many years in systems such as molecular oscillators, 10 electronic circuits, 11 Van der Pol oscillators, 12 traffic models, 13 optically and optoelectronically coupled semiconductor lasers, and in generic model systems such as phase oscillators 14 or logistic maps. 15 The early investigations could, however, only address the situations of small delays and weak nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Amplitude and phase effects on the synchronization of delay-coupled oscillators

D'Huys

Vicente

Danckaert

et al. 2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We consider the behavior of Stuart-Landau oscillators as generic limit-cycle oscillators when they are interacting with delay. We investigate the role of amplitude and phase instabilities in producing symmetry-breaking/restoring transitions. Using analytical and numerical methods we compare the dynamics of one oscillator with delayed feedback, two oscillators mutually coupled with delay, and two delay-coupled elements with self-feedback. Taking only the phase dynamics into account, no chaotic dynamics is observed, and the stability of the identical synchronization solution is the same in each of the three studied networks of delay-coupled elements. When allowing for a variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability always results in antiphase oscillations, leading to a leader-laggard behavior in the chaotic regime. Adding self-feedback with the same strength and delay as the coupling stabilizes the system in the transverse direction and, thus, promotes the onset of identically synchronized behavior.

show abstract

Section: Introductionmentioning

confidence: 99%

Amplitude and phase effects on the synchronization of delay-coupled oscillators

D'Huys

Vicente

Danckaert

et al. 2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…Equations (17) and (18) show that there are two possibilities: r = 0 or r = 0. When r = 0, Eqs (17) and 18become…”

Section: Steady-state Resonancementioning

confidence: 99%

“…Masccari [17] studied the parametric resonance of van der pol oscillator under state feedback control with time delay. Kouda and Mori [18] investigated the analysis of a ring of mutually coupled van der pol oscillators with coupling delay. Kouda and Mori [18] investigated the analysis of a ring of mutually coupled van der pol oscillators with coupling delay.…”

Section: Introductionmentioning

confidence: 99%

“…Kouda and Mori [18] investigated the analysis of a ring of mutually coupled van der pol oscillators with coupling delay. Kouda and Mori [18] investigated the analysis of a ring of mutually coupled van der pol oscillators with coupling delay. Faria [19] investigated stability and bifurcation for a delayed predator for a delayed predator-prey model and effect of diffusion.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

El-Bassiouny

2005

Shock and Vibration

View full text Add to dashboard Cite

Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.

show abstract

“…ElBassiouny [20] investigated fundamental and subharmonic resonances of harmonical oscillation with delay state feedback. Kouda and Mori [21] analyzed a ring of mutually coupled van der Pol oscillators with coupling delay. Oueni et al [22] have considered a nonlinear active vibration absorber coupled with the plant through user-defined cubic nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Vibration Control of a Cantilever Beam with Time Delay State Feedback

El-Bassiouny

2006

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

The primary and subharmonic resonance of order one-third of a cantilever beam under state feedback control with a time delay are investigated. Using the method of multiple scales, we obtain two slow flow equations for the amplitude and phase. The first-order approximate solution is derived and the effect of time delay on the resonance is investigated. The concept of an equivalent damping, related to the delay feedback, is proposed and an appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The fixed points corresponding to the periodic motion of the starting system are determined, and the frequency-response and external excitation-response curves are shown. Bifurcation analysis is conducted in order to examine the stability of the system.

show abstract

Analysis of a ring of mutually coupled van der Pol oscillators with coupling delay

Cited by 11 publications

References 7 publications

Amplitude and phase effects on the synchronization of delay-coupled oscillators

Amplitude and phase effects on the synchronization of delay-coupled oscillators

Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

Vibration Control of a Cantilever Beam with Time Delay State Feedback

Contact Info

Product

Resources

About