| Full text | |
| Author(s): |
da Costa, Fabio H.
;
de Almeida, Mayla A. M.
;
Medrano-T, Rene O.
;
Leonel, Edson D.
;
de Oliveira, Juliano A.
Total Authors: 5
|
| Document type: | Journal article |
| Source: | Chaos; v. 34, n. 12, p. 9-pg., 2024-12-01. |
| Abstract | |
A family of dissipative two-dimensional nonlinear mappings is considered. The mapping is described by the angle and action variables and parameterized by epsilon controlling nonlinearity, delta controlling the amount of dissipation, and an exponent gamma is a dynamic free parameter that enables a connection with various distinct dynamic systems. The Lyapunov exponents are obtained for different values of the control parameters to characterize the chaotic attractors. We investigated the time evolution for the stationary state at period-doubling bifurcations. The convergence to the stationary state is made using a robust homogeneous and generalized function at the bifurcation parameter, which leads us to obtain a set of universal critical exponents. The parameter space of the mapping is investigated, and tangent, period-doubling, pitchfork, and cusp bifurcations are found, and a street of saddle-area and spring-area structures is observed. (AU) | |
| FAPESP's process: | 24/06718-5 - Basins of Attraction: From unidimensional maps to complex networks |
| Grantee: | Rene Orlando Medrano Torricos |
| 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: | 19/14038-6 - Investigation of dynamical properties in nonlinear systems |
| Grantee: | Edson Denis Leonel |
| 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 |