Coupled van der Pol–Duffing oscillators: Phase dynamics and structure of synchronization tongues

Кузнецов, А. П.; Stankevich, Nataliya; Turukina, Ludmila V.

doi:10.1016/j.physd.2009.04.001

Cited by 81 publications

(71 citation statements)

References 20 publications

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“…Coherent coupling leads to much weaker phase locking than dissipative coupling and generates a relative phase distribution which is π-periodic rather than 2π-periodic. This matches the well-known differences in relative phase dynamics of reactively and dissipatively coupled classical oscillators which are usually understood by deriving approximate equations of motion for the relative phase of the oscillator assuming weak coupling [1,34]. …”

Section: Relative Phase Distributionsupporting

confidence: 77%

“…As is the case for classical oscillators [1,33,34], the behavior can be very sensitive to the form of the coupling as well as its strength. We investigate two specific forms for the coupling involving either additional terms in the Hamiltonian of the system (coherent coupling) or additional dissipative terms in the master equation (dissipative coupling).…”

Section: Micromaser Modelmentioning

confidence: 99%

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Synchronization of micromasers

Davis-Tilley

Armour

2016

Phys. Rev. A

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We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of preferred phases when two micromasers are coupled together. Using perturbation theory, we show that the behavior of the phase distribution is strongly dependent on exactly how the oscillators are coupled. In the quantum regime where photon occupation numbers are low we find that although synchronization effects are rather weak, they are nevertheless significantly stronger than expected from a semiclassical description of the phase dynamics. We also compare the behavior of the phase distribution with the mutual information of the two oscillators and show that they can behave in rather different ways.

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Section: Relative Phase Distributionsupporting

confidence: 77%

Section: Micromaser Modelmentioning

confidence: 99%

Synchronization of micromasers

Davis-Tilley

Armour

2016

Phys. Rev. A

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“…В частности, в работе [9] исследовалась синхронизация простой модели двух осцилляторов с предельным циклом, связанных с задержкой. Как известно, в подоб-ной системе можно выделить два основных типа связи: диссипативную (диффузионную) и инерционную (реактивную) [10,11]. Эти случаи отличаются устройством областей синхро-низации в пространстве параметров, в которых синхронный режим является устойчивым, причем при инерционной связи режим синхронизации становится бистабильным: возможна синхронизация как на синфазной, так и на противофазной моде.…”

Section: а б адилова с а герасимова н м рыскинunclassified

Bifurcation analysis of mutual synchronization of two oscillators coupled with delay

Булатовна¹,

Gerasimova²,

Ryskin³

2017

Nelin. Dinam.

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“…1), made of two oscillators of mass m 1 and m 2 , respectively, linked each other and to the ground by cubic elastic springs and Van Der Pol dampers. It represents a class of coupled Duffing-Van Der Pol oscillators (see [22][23][24][25][26][27][28]). The linear coefficients of the springs and of the dashpots are denoted by k i1 and c i1 , respectively, and their cubic coefficients by k i3 and c i3 (i = 0, 1, 2).…”

Section: The Modelmentioning

confidence: 99%