2011
DOI: 10.1103/physreve.84.016226
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Phase-flip transition in relay-coupled nonlinear oscillators

Abstract: We study the dynamics of oscillators that are coupled in relay; namely, through an intermediary oscillator. From previous studies it is known that the oscillators show a transition from in-phase to out-of-phase oscillations or vice versa when the interactions involve a time delay. Here we show that, in the absence of time delay, relay coupling through conjugate variables has the same effect. However, this phase-flip transition does not occur abruptly at a certain critical value of the coupling parameter. Inste… Show more

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Cited by 43 publications
(21 citation statements)
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“…For asymmetric time-delays, even in the case of two coupled oscillators, the phase difference can be different from π [67]. Such different phase relations have been seen in experiments with asymmetric coupling [106] and time-delay [67] as well as in in relay-coupled nonlinear oscillators [79].…”
Section: The Phase-flipmentioning
confidence: 86%
See 1 more Smart Citation
“…For asymmetric time-delays, even in the case of two coupled oscillators, the phase difference can be different from π [67]. Such different phase relations have been seen in experiments with asymmetric coupling [106] and time-delay [67] as well as in in relay-coupled nonlinear oscillators [79].…”
Section: The Phase-flipmentioning
confidence: 86%
“…Apart from above discussed scenarios, other situations where amplitude death occurs include the case of indirect coupling [49,78,79]: when two oscillators are coupled via a third, the presence of the intermediate system causes an effective "transmission" delay, which then effects amplitude death. It has been also suggested [78] that the AD is due to competition between synchronization and anti synchronization.…”
Section: Linear Augmentation and Other Strategiesmentioning
confidence: 99%
“…For each node, ω i + (x i 2 + y i 2 ) is close to the angular velocity of the i th oscillator, perturbed by amplitude x i 2 + y i 2 when = 0. Here we take the parameter values to be: a = 0.15, b = 0.4, c = 8.5, ω 1 = ω 2 = ω 3 = 0.41 and = 0.0026 [24], yielding a chaotic attractor. We also consider the Lorenz system at the nodes given by:…”
Section: Star Network Of Chaotic Oscillatorsmentioning
confidence: 99%
“…The dynamical system with conjugate coupling has been used to realize the amplitude death [10,11] in coupled identical units, the phenomenon in which unstable equilibrium in isolated unit becomes stable with the assistance of the coupling, in several recent works [12][13][14]. Interestingly, the realized amplitude death has indeed referred that synchronization in oscillators with conjugate coupling is possible but the synchronous state is not necessarily a stable solution of isolated units.…”
mentioning
confidence: 99%