Synchronization in a Ring of Oscillators with Delayed Feedback

A ring of coupled oscillators with delayed feedback with various types of coupling between the oscillators is considered. For each type of coupling, the asymptotic behavior of the model solutions with respect to a large parameter is constructed for a wide variety of initial conditions. It is shown t...

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Bibliographic Details
Published in:Mathematical Notes 2024-06, Vol.115 (5-6), p.944-958
Main Author: Kashchenko, A. A.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
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Asymptotic properties
Coupling
Feedback
Initial conditions
Mathematics
Mathematics and Statistics
Oscillators
Parameters
Synchronism
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Summary:A ring of coupled oscillators with delayed feedback with various types of coupling between the oscillators is considered. For each type of coupling, the asymptotic behavior of the model solutions with respect to a large parameter is constructed for a wide variety of initial conditions. It is shown that the studying the behavior of solutions to the original infinite-dimensional models can be reduced to studying the dynamics of the constructed finite-dimensional mappings. High quality conclusions about the dynamics of the original systems are made. It is shown that the behavior of solutions significantly varies with variations in the type of coupling. Conditions on the system parameters are found under which the synchronization, two-cluster synchronization, and more complex modes are possible.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434624050298