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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Trapping Phenomenon Attenuates the Consequences of Tipping Points for Limit Cycles

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Medeiros, Everton S. ; Caldas, Ibere L. ; Baptista, Murilo S. ; Feudel, Ulrike
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: SCIENTIFIC REPORTS; v. 7, FEB 9 2017.
Citações Web of Science: 11

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the system's parameters abruptly shift the system to an alternative state with a contrasting dynamical behavior. While tipping in a fold bifurcation of an equilibrium is well understood, much less is known about tipping of oscillations (limit cycles) though this dynamics are the typical response of many natural systems to a periodic external forcing, like e.g. seasonal forcing in ecology and climate sciences. We provide a detailed analysis of tipping phenomena in periodically forced systems and show that, when limit cycles are considered, a transient structure, so-called channel, plays a fundamental role in the transition. Specifically, we demonstrate that trajectories crossing such channel conserve, for a characteristic time, the twisting behavior of the stable limit cycle destroyed in the fold bifurcation of cycles. As a consequence, this channel acts like a ``ghost{''} of the limit cycle destroyed in the critical transition and instead of the expected abrupt transition we find a smooth one. This smoothness is also the reason that it is difficult to precisely determine the transition point employing the usual indicators of tipping points, like critical slowing down and flickering. (AU)

Processo FAPESP: 13/26598-0 - Caracterização das Fronteiras entre Periodicidade e Caos no Espaço de Parâmetros
Beneficiário:Everton Santos Medeiros
Linha de fomento: Bolsas no Brasil - Pós-Doutorado
Processo FAPESP: 15/20407-3 - Investigando as consequências de transições abruptas em sistemas dinâmicos
Beneficiário:Everton Santos Medeiros
Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
Processo FAPESP: 11/19296-1 - Dinâmica não linear
Beneficiário:Iberê Luiz Caldas
Linha de fomento: Auxílio à Pesquisa - Temático