%0 Journal Article %1 WOS:000356121800021 %A Leonel, Edson D %A Teixeira, Rivania M N %A Rando, Danilo S %A Filho, R N Costa %A de Oliveira, Juliano A %C PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS %D 2015 %I ELSEVIER SCIENCE BV %J PHYSICS LETTERS A %K Critical Homogeneous exponents; function} law; {Scaling %N 30-31 %P 1796-1798 %R 10.1016/j.physleta.2015.05.002 %T Convergence towards asymptotic state in 1-D mappings: A scaling investigation (vol 379, pg 1246, 2015) %V 379 %X 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 mu = R - R-c where R-c is the bifurcation parameter. We found here the exponents alpha, beta, z and delta analytically, confirming our numerical simulations shown in 1. (C) 2015 Elsevier B.V. All rights reserved.

@article{WOS:000356121800021, 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 mu = R - R-c where R-c is the bifurcation parameter. We found here the exponents alpha, beta, z and delta analytically, confirming our numerical simulations shown in [1]. (C) 2015 Elsevier B.V. All rights reserved.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}, author = {Leonel, Edson D and Teixeira, Rivania M N and Rando, Danilo S and Filho, R N Costa and de Oliveira, Juliano A}, biburl = {https://www.bibsonomy.org/bibtex/284e43ac46e502df5adeadeff60562a5f/ppgfis_ufc_br}, doi = {10.1016/j.physleta.2015.05.002}, interhash = {44b05080cb232a463e71372da493e527}, intrahash = {84e43ac46e502df5adeadeff60562a5f}, issn = {0375-9601}, journal = {PHYSICS LETTERS A}, keywords = {Critical Homogeneous exponents; function} law; {Scaling}, number = {30-31}, pages = {1796-1798}, publisher = {ELSEVIER SCIENCE BV}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Convergence towards asymptotic state in 1-D mappings: A scaling investigation (vol 379, pg 1246, 2015)}, tppubtype = {article}, volume = 379, year = 2015 }