Nonlinear complexification of periodic orbits in the generalized Landau scenario
dc.contributor.author
dc.date.accessioned
2022-02-15T08:36:24Z
dc.date.available
2022-02-15T08:36:24Z
dc.date.issued
2022-02-10
dc.identifier.issn
1054-1500
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dc.description.abstract
We have found a way for penetrating the space of the dynamical systems toward systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions may arise. The system design is based on assuring the occurrence of a number of Hopf bifurcations in a set of fixed points of a relatively generic system of ordinary differential equations, in which the main peculiarity is that the nonlinearities appear through functions of a linear combination of the system variables. The paper outlines the design procedure and presents a selection of numerical simulations with a variety of designed systems whose dynamical behaviors are really rich and full of unknown features. For concreteness, the presentation is focused on illustrating the oscillatory mixing effects on the periodic orbits, through which the harmonic oscillation born in a Hopf bifurcation becomes successively enriched with the intermittent incorporation of other oscillation modes of higher frequencies while the orbit remains periodic and without the necessity of bifurcating instabilities. Even in the absence of a proper mathematical theory covering the nonlinear mixing mechanisms, we find enough evidence to expect that the oscillatory scenario be truly scalable concerning the phase-space dimension, the multiplicity of involved fixed points, and the range of time scales so that extremely complex but ordered dynamical behaviors could be sustained through it
dc.format.extent
24 p.
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application/pdf
dc.language.iso
eng
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Versió postprint del document publicat a: https://doi.org/10.1063/5.0069878
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© Chaos, 2022, vol. 32, art.núm. 023116, p. 1-24
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Articles publicats (D-F)
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Tots els drets reservats
dc.source
Herrero, Ramon Farjas Silva, Jordi Pi, Francesc Orriols, Gaspar 2022 Nonlinear complexification of periodic orbits in the generalized Landau scenario Chaos 32 art.núm. 023116 1 24
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dc.title
Nonlinear complexification of periodic orbits in the generalized Landau scenario
dc.type
info:eu-repo/semantics/article
dc.rights.accessRights
info:eu-repo/semantics/openAccess
dc.type.version
info:eu-repo/semantics/publishedVersion
dc.identifier.doi
dc.identifier.idgrec
034900
dc.type.peerreviewed
peer-reviewed
dc.identifier.eissn
1089-7682