Basins of Attraction: From unidimensional maps to complex networks
Study of the origin of unsteadiness in unforced three-dimensional laminar separati...
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| Full text | |
| Author(s): |
Mihara, Antonio
;
Zaks, Michael
;
Macau, Elbert E. N.
;
Medrano-T, Rene O.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW E; v. 105, n. 5, p. 5-pg., 2022-05-05. |
| Abstract | |
We show that for the Kuramoto model (with identical phase oscillators equally coupled), its global statistics and size of the basins of attraction can be estimated through the eigenvalues of all stable (frequency) synchronized states. This result is somehow unexpected since, by doing that, one could just use a local analysis to obtain the global dynamic properties. But recent works based on Koopman and Perron-Frobenius operators demonstrate that the global features of a nonlinear dynamical system, with some specific conditions, are somehow encoded in the local eigenvalues of its equilibrium states. Recognized numerical simulations in the literature reinforce our analytical results. (AU) | |
| FAPESP's process: | 15/50122-0 - Dynamic phenomena in complex networks: basics and applications |
| Grantee: | Elbert Einstein Nehrer Macau |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/03517-8 - Association between heart rate variability and salivary cortisol for the evaluation of individuals under stress conditions by means of nonlinear analysis and artificial intelligence methods |
| Grantee: | Laurita dos Santos |
| Support Opportunities: | Regular Research Grants |