Universal behavior of the convergence to the stationary state for a tangent bifurcation in the logistic map

• Autor(a) principal: Hermes, Joelson D.V.
• Data de Publicação: 2020
• Outros Autores: Graciano, Flávio Heleno, Leonel, Edson D. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.5890/DNC.2020.03.005; http://hdl.handle.net/11449/198514
• topic: Critical exponents; Logistic map; Tangent bifurcation

The scaling formalism is applied to understand and describe the evolution towards the equilibrium at and near at a tangent bifurcation in the logistic map. At the bifurcation the convergence to the steady state is described by a homogeneous function leading to a set of critical exponents. Near the bifurcation the convergence is rather exponential whose relaxation time is given by a power law. We use two different approaches to obtain the critical exponents: (1) a phenomenological investigation based on three scaling hypotheses leading to a scaling law relating three critical exponents and; (2) an approximation that transforms the recurrence equations in a differential equation which is solved under appropriate conditions given analytically the scaling exponents. The numerical results give support for the theoretical approach.