Hierarchy of partially synchronous states in a ring of coupled identical oscillators.
Phys Rev E
; 108(3-1): 034202, 2023 Sep.
Article
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| MEDLINE
| ID: mdl-37849175
ABSTRACT
In coupled identical oscillators, complete synchronization has been well formulated; however, partial synchronization still calls for a general theory. In this work, we study the partial synchronization in a ring of N locally coupled identical oscillators. We first establish the correspondence between partially synchronous states and conjugacy classes of subgroups of the dihedral group D_{N}. Then we present a systematic method to identify all partially synchronous dynamics on their synchronous manifolds by reducing a ring of oscillators to short chains with various boundary conditions. We find that partially synchronous states are organized into a hierarchical structure and, along a directed path in the structure, upstream partially synchronous states are less synchronous than downstream ones.
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01-internacional
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MEDLINE
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En
Revista:
Phys Rev E
Año:
2023
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Article