Ensembles of four discrete phase oscillators

Мұқаба

Дәйексөз келтіру

Толық мәтін

Аннотация

Background and Objectives: Ensembles of four discrete phase oscillators are considered. The aim of the research is to study and compare ensembles with different topologies of coupling: chains, rings and stars. Materials and Methods: We carry out the analysis using three-dimensional discrete maps for the relative phases of oscillators. We use the method of Lyapunov exponent chart, which identifies periodic regimes, quasi-periodic regimes with a different number of incommensurable frequencies and chaos. The various modes are illustrated using phase portraits. Results: We have found the regions of different regimes in the frequency detuning space of oscillators for different topologies of coupling. Resonances are indicated and illustrated both for pairs and for triples of synchronized oscillators, which corresponds to three- and two-frequency quasi-periodicity. We observe Arnold resonance web based on four frequency as well as on chaotic regimes. Conclusion: The ensemble of four discrete phase oscillators demonstrates a variety of quasi-periodic regimes with a different number of incommensurable frequencies, which are caused by possible resonances depending on the topology of coupling.

Авторлар туралы

Alexander Kuznetsov

Saratov Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences

ORCID iD: 0000-0001-5528-1979
SPIN-код: 5807-1180
38, Zelenaya Str., Saratov 410019, Russia

Yuliya Sedova

Saratov Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences

ORCID iD: 0000-0001-7843-646X
SPIN-код: 1312-1957
38, Zelenaya Str., Saratov 410019, Russia

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