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Synchronization and Multicluster Capabilities of Oscillatory Networks With Adaptive Coupling
- Source :
- IEEE Transactions on Automatic Control. 66:3084-3096
- Publication Year :
- 2021
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2021.
-
Abstract
- We prove the existence of a multidimensional nontrivial invariant toroidal manifold for the Kuramoto network with adaptive coupling. The constructed invariant manifold corresponds to the multicluster behavior of the oscillators phases. Contrary to the static coupling, the adaptive coupling strengths exhibit quasiperiodic oscillations preserving zero phase-difference within clusters. The derived sufficient conditions for the existence of the invariant manifold provide a tradeoff between the natural frequencies of the oscillators, coupling plasticity parameters, and the interconnection structure of the network. Furthermore, we study the robustness of the invariant manifold with respect to the perturbations of the interconnection topology, and establish structural, and quantitative constraints on the perturbation adjacency matrix preserving the invariant manifold. Additionally, we demonstrate the application of the new results to the problem of interconnection topology design, which consists in endowing the desired multicluster behavior to the network by controlling its interconnection structure.
- Subjects :
- Coupling
Physics
0209 industrial biotechnology
Interconnection
Invariant manifold
02 engineering and technology
Topology
Manifold
Computer Science Applications
020901 industrial engineering & automation
Control and Systems Engineering
Robustness (computer science)
Quasiperiodic function
Adjacency matrix
Electrical and Electronic Engineering
Invariant (mathematics)
Subjects
Details
- ISSN :
- 23343303 and 00189286
- Volume :
- 66
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Automatic Control
- Accession number :
- edsair.doi...........95a41285a3d4b980d3f5d1a63ea50df0