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| Author(s): |
Hans Muller Junho de Mendonça
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Rio Claro. 2018-05-16. |
| Institution: | Universidade Estadual Paulista (Unesp). Instituto de Geociências e Ciências Exatas. Rio Claro |
| Defense date: | 2018-02-28 |
| Advisor: | Juliano Antonio de Oliveira |
| Abstract | |
In this work we study the decay of the orbits to the xed points in di erent bifurcations of nonlinear discrete one-dimensional mappings. We consider the Gauss map and analyze the orbit diagram to study the convergence of the trajectories to the equilibrium point at the fold and ip bifurcation. We nd numerically and analytically the set of critical exponents that describe some scaling properties at the bifurcations and near them. These critical exponents can also characterize which types of bifurcations that arises from the problem in question. We also study particular events called boundary crisis that occur from above a speci c value of the control parameter . We continue the studies considering the Hassell map and its perturbed version. Just like in the Gauss map, we analyze the orbit diagrams within these systems, as well as the convergence of the orbits to the xed points at the transcritical bifurcations, while also investigating numerically and analytically to determine the speci c critical exponents of those bifurcations. With parametric perturbation added to the Hassell map, we build and analyze the trajectories on the parameter space. We apply, as tools, the superstable and extreme orbits. In the two classes of the maps (Gauss and Hassell), we quantify the chaos by Lyapunov exponents. After the critical exponents are obtained, using convenient scale transformations in the coordinate axes we show that all the curves of decay to the xed points are collapsed into a universal curve, thus validating the exponents. (AU) | |
| FAPESP's process: | 15/22062-3 - Scaling properties and cascades bifurcations in one-dimensional discrete maps |
| Grantee: | Hans Muller Junho de Mendonça |
| Support Opportunities: | Scholarships in Brazil - Master |