Trapping Phenomenon Attenuates the Consequences of Tipping Points for Limit Cycles

Autor(es)

Medeiros, Everton S. ; Caldas, Ibere L. ; Baptista, Murilo S. ; Feudel, Ulrike

• Tipo de documento: Artigo Científico
• Fonte: SCIENTIFIC REPORTS; v. 7, FEB 9 2017.
• Citações Web of Science: 11

Resumo

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
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 15/20407-3 - Investigando as consequências de transições abruptas em sistemas dinâmicos
• Beneficiário: Everton Santos Medeiros
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 11/19296-1 - Dinâmica não linear
• Beneficiário: Iberê Luiz Caldas
• Modalidade de apoio: Auxílio à Pesquisa - Temático