| Full text | |
| Author(s): |
Leonel, Edson D.
[1, 2]
Total Authors: 1
|
| Affiliation: | [1] Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste - Italy
[2] Univ Estadual Paulista, UNESP, Dept Fis, Av 24A, 1515 Bela Vista, BR-13506900 Rio Claro, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION; v. 39, p. 520-528, OCT 2016. |
| Web of Science Citations: | 1 |
| Abstract | |
The convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents alpha, beta and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent delta. The four exponents alpha, beta, z and delta can be used to defined classes of universality for the local bifurcations of fixed points in differential equations. (C) 2016 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 12/23688-5 - Exponents and scaling laws, phase transitions and transport properties of time dependent systems |
| Grantee: | Edson Denis Leonel |
| Support Opportunities: | Regular Research Grants |