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Journal article
Bifurcations and Patterns in the Kuramoto Model with Inertia
JOURNAL OF NONLINEAR SCIENCE, v 33(5), 78
Oct 2023
Abstract
In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampled from a probability distribution. In addition, a given graph, which may also be random, assigns network connectivity. As in the original KM, in the model with inertia, the weak coupling regime features mixing, the state of the network when the phases (but not velocities) of all oscillators are distributed uniformly around the unit circle. We study patterns, which emerge when mixing loses stability under the variation of the strength of coupling. We identify a pitchfork (PF) and an Andronov-Hopf (AH) bifurcations in the model with multimodal intrinsic frequency distributions. To this effect, we use a combination of the linear stability analysis and Penrose diagrams, a geometric technique for studying stability of mixing. We show that the type of a bifurcation and a nascent spatiotemporal pattern depend on the interplay of the qualitative properties of the intrinsic frequency distribution and network connectivity.
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Details
- Title
- Bifurcations and Patterns in the Kuramoto Model with Inertia
- Publication Details
- JOURNAL OF NONLINEAR SCIENCE, v 33(5), 78
- Publisher
- SPRINGER; NEW YORK
- Grant note
- This work was supported by JST Moonshot Research and Development Grant No. JPMJMS2023 (to HC), NSF Grant DMS 2009233 (to GSM), and by Support of Scholarly Activities Grant at The College of New Jersey (to MSM). Numerical simulations were completed using the high performance computing cluster (ELSA) at the School of Science, The College of New Jersey. Funding of ELSA is provided in part by NSF OAC-1828163.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:001022962300001
- Scopus ID
- 2-s2.0-85163950395
- Other Identifier
- 991021861163904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied
- Mechanics
- Physics, Mathematical