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| Author(s): |
Murilo da Silva Baptista
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física (IF/SBI) |
| Defense date: | 1996-11-14 |
| Examining board members: |
Ibere Luiz Caldas;
Marcus Aloizio Martinez de Aguiar;
Clodoaldo Grotta Ragazzo;
Jose Carlos Sartorelli;
Ricardo Luiz Viana
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| Advisor: | Ibere Luiz Caldas |
| Abstract | |
Initially, we consider the Logistic map with its many non-linear phenomena. Then, we use this knowledge to discern new phenomena that shall appear when the map is perturbed, that is the Logistic map perturbed by a periodic and constant term. The Matsumoto\'s circuit is presented and, after we set this circuit to behave chaotically, we perturb it with a sinoidal wave, characterized by its frequency and amplitude. This perturbation is responsible for the appearence of a quasi-periodic and periodic oscillations, or the maintenance of chaos. We presented and applied many methods for controlling chaotic oscillations in three systems (the Logistic and Henon maps, and the Matsumoto\'s circuit), showing many ways for stabilizing a periodic orbit, using the methods of Ott-Grebogi-York (OGY), Romeiras, Singer, Sinhas and Huebbler. For targeting the trajectory to a equilibrium point, the Sinha\'s method was used. To transfer the system trajectory from one to another of the coexisting attractors presented in the Matsumoto\'s circuit, we use the Jackson-Huebbler (OPCL) method. Using a set of constant perturbations, in a previously chosen parameter, we showed how we can rapidly direct a trajectory of any of the considered three systems to a aimed target. Besides, it is shown how this method can be experimentally applied. (AU) | |