| Full text | |
| Author(s): |
de Almeida, Mayla A. M.
;
Costa, Fabio H.
;
Leonel, Edson D.
;
de Oliveira, Juliano A.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | European Physical Journal-Special Topics; v. N/A, p. 10-pg., 2025-08-26. |
| Abstract | |
A two-dimensional nonlinear mapping described in the action and angle variables is considered. The mapping is parameterized by a control parameter that controls the intensity of nonlinearity, by a parameter controlling the amount of dissipation, and by a dynamical exponent such that for certain choices of its values and naming the action and angle variables, we recover different mappings known in the literature. Our main research focus was to analyze the convergence of orbits to the steady state through a robust phenomenological description of the scaling approach at bifurcation, which led us to obtain a set of critical exponents that define universality classes of bifurcations. We advanced our studies using Lyapunov exponents to characterize chaos and carefully investigate the phenomenon known as boundary crises to analyze the crossing of stable and unstable manifolds. (AU) | |
| FAPESP's process: | 19/14038-6 - Investigation of dynamical properties in nonlinear systems |
| Grantee: | Edson Denis Leonel |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/14685-9 - Transport properties and bifurcation analysis in nonlinear dynamical systems |
| Grantee: | Juliano Antonio de Oliveira |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 21/09519-5 - Characterization of phase transitions in nonlinear systems |
| Grantee: | Edson Denis Leonel |
| Support Opportunities: | Regular Research Grants |