ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kulminskiy D. D., Ponomarenko V. I., Prokhorov M. D. Influence of inertial properties and delay of the mean field on the collective dynamics of globally coupled bistable delayed-feedback oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2018, vol. 26, iss. 1, pp. 4-20. DOI: 10.18500/0869-6632-2018-26-1-4-20

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
537.86
DOI: 
10.18500/0869-6632-2018-26-1-4-20

Influence of inertial properties and delay of the mean field on the collective dynamics of globally coupled bistable delayed-feedback oscillators

Autors: 
Kulminskiy Danil Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

The features of collective dynamics of oscillators are studied in an ensemble of identical bistable time-delay systems globally coupled via the mean field. The influence of inertial proper-ties and delay of the mean field on the collective dynamics of oscillators is considered. It is shown that a variety of oscillation regimes in the ensemble is caused by the presence of bistable states with considerably different basic frequencies in coupled oscillators. Under the correspond-ing choice of the mean field parameters, it allows us to ensure different phase shifts of the mean field signal for oscillators in different regimes of oscillations. It is shown that under a specific choice of initial conditions, two clusters are formed in the ensemble. Depending on the phase shift of the mean field, each of these clusters can contain either synchronous or asynchronous oscillators. If the coupling is attractive for oscillators in one cluster and repulsive for oscillators in another cluster, a chimera state takes place in the ensemble, in which a cluster with synchronized oscillators coexists with a cluster with non-synchronized oscillators. The obtained results can be useful for solving the problem of controlling the oscillation regimes in the networks of globally coupled oscillators in situations, where it is possible to vary the mean field parameters.

Key words: 
ensembles of coupled oscillators
clusterization
synchronization
Time-delay systems
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Received: 
16.08.2017
Accepted: 
27.10.2017
Published: 
28.02.2018
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