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

Abstract

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].