Dynamical mechanism behind ghosts unveiled in a map complexification
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Otros documentos de la autoría: Canela, Jordi; Alsedà i Soler, Lluís; Fagella, Núria; Sardanes, JOSEP
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Título
Dynamical mechanism behind ghosts unveiled in a map complexificationFecha de publicación
2022-01-14Editor
ElsevierCita bibliográfica
CANELA, Jordi, et al. Dynamical mechanism behind ghosts unveiled in a map complexification. Chaos, Solitons & Fractals, 2022, vol. 156, p. 111780.Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/submittedVersionPalabras clave / Materias
Resumen
Complex systems such as ecosystems, electronic circuits, lasers, or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. It is known that transients become extremely long ... [+]
Complex systems such as ecosystems, electronic circuits, lasers, or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. It is known that transients become extremely long close to bifurcations, also following well-defined scaling laws as the bifurcation parameter gets closer the bifurcation value. For saddle-node bifurcations, the dynamical mechanism responsible for these delays, tangible at the real numbers phase space (so-called ghosts), occurs at the complex phase space. To study this phenomenon we have complexified an ecological map with a saddle-node bifurcation. We have investigated the complex (as opposed to real) dynamics after this bifurcation, identifying the fundamental mechanism causing such long delays, given by the presence of two repellers in the complex space. Such repellers appear to be extremely close to the real line, thus forming a narrow channel close to the two new fixed points and responsible for the slow passage of the orbits. We analytically provide the relation between the well-known inverse square-root scaling law of transient times and the multipliers of these repellers. We finally prove that the same phenomenon occurs for more general i.e. non-necessarily polynomial, models. [-]
Publicado en
Chaos, Solitons & Fractals Vol. 156, March 2022Entidad financiadora
Spanish State Research Agency (AEI), Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D | CERCA Programme / Generalitat de Catalunya | Spanish Ministry of Economy and Competitiveness, María de Maeztu Programme | BGSMath Banco de Santander Postdoctoral fellowship | Universitat Jaume I | Ministerio de Ciencia, Innovación y Universidades (Spain) | MTM2017-86795-C3-3-P | Generalitat de Catalunya | Ramón y Cajal contract
Código del proyecto o subvención
CEX2020-001084-M | MDM-2014-0445 | UJI-B2019-18 | PID2020-118281GB-C32 | 2017SGR1374 | ICREA Acadèmia 2020 | PID2020-118281GB-C31 | MTM2017-86795-C3-1-P | RTI2018-098322-B-I00 | RYC-2017-22243
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