Kuramoto variables as eigenvalues of unitary matrices
Marcel Novaes, Marcus A. M. de Aguiar
ARTIGO
Inglês
Agradecimentos: This work was supported by FAPESP, Grants No. 2021/14335-0 (M.A.M.A.) and No. 2023/15644-2 (M.N. and M.A.M.A.) and also by CNPq, Grants No. 301082/2019-7 (M.A.M.A.) and No. 304986/2022-4 (M.N.)
Abstract: We generalize the Kuramoto model by interpreting the N variables on the unit circle as eigenvalues of a N-dimensional unitary matrix U in three versions: general unitary, symmetric unitary, and special orthogonal. The time evolution is generated by N2 coupled differential equations for the...
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Abstract: We generalize the Kuramoto model by interpreting the N variables on the unit circle as eigenvalues of a N-dimensional unitary matrix U in three versions: general unitary, symmetric unitary, and special orthogonal. The time evolution is generated by N2 coupled differential equations for the matrix elements of U, and synchronization happens when U evolves into a multiple of the identity. The Ott-Antonsen ansatz is related to the Poisson kernels that are so useful in quantum transport, and we prove it in the case of identical natural frequencies. When the coupling constant is a matrix, we find some surprising new dynamical behaviors
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FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP
2021/14335-0; 2023/15644-2
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ
301082/2019-7; 304986/2022-4
Fechado
Kuramoto variables as eigenvalues of unitary matrices
Marcel Novaes, Marcus A. M. de Aguiar
Kuramoto variables as eigenvalues of unitary matrices
Marcel Novaes, Marcus A. M. de Aguiar
Fontes
Physical review. E, Covering statistical, nonlinear, biological, and soft matter physics (Fonte avulsa) |