Critical Slowing Down at a Fold and a Period Doubling Bifurcations for a Gauss Map

• Autor(a) principal: de Oliveira, Juliano A. [UNESP]
• Data de Publicação: 2019
• Outros Autores: de Mendonça, Hans M. J. [UNESP], da Silva, Anderson A. A. [UNESP], Leonel, Edson D. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s13538-019-00706-0; http://hdl.handle.net/11449/199664
• topic: Bifurcations; Critical exponents; Gauss map; Scaling law

The convergence to the stationary state is described using scaling arguments at a fold and a period doubling bifurcation in a one-dimensional Gauss map. Two procedures are used: (i) a phenomenological investigation leading to a set of critical exponents defining the universality class of the bifurcation and; (ii) analytical investigation that transforms, near the stationary state, the difference equation into an ordinary differential equation that is easily solved. The novelty of the procedure comes from the fact that it is firstly applied to the Gauss map and critical exponents for the fold bifurcations are defined.