Addendum to: Convergence towards asymptotic state in 1-D mappings: A scaling investigation [Phys. Lett. A 379 (2015) 1246]

• Main Author: Leonel, Edson D. [UNESP]
• Publication Date: 2015
• Other Authors: Teixeira, Rivania M.N., Rando, Danilo S. [UNESP], Costa Filho, R. N., De Oliveira, Juliano A. [UNESP]
• Format: Other
• Language: eng
• Source: Repositório Institucional da UNESP
• Download full: http://dx.doi.org/10.1016/j.physleta.2015.05.002; http://hdl.handle.net/11449/167924
• topic: Critical exponents; Homogeneous function; Scaling law

An analytical description of the convergence to the stationary state in period doubling bifurcations for a family of one-dimensional logistic-like mappings is made. As reported in [1], at a bifurcation point, the convergence to the fixed point is described by a scaling function with well defined critical exponents. Near the bifurcation, the convergence is characterized by an exponential decay with the relaxation time given by a power law of μ=R - Rc where Rc is the bifurcation parameter. We found here the exponents α, β, z and δ analytically, confirming our numerical simulations shown in [1].