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Previous issue date: 2012-08 / O circuito RLD, formado por um resistor, um indutor e um diodo em s?rie, apresenta uma din?mica muito rica quando for?ado por uma tens?o externa harm?nica e vem sendo estudado h? d?cadas. Contudo, ainda existem t?picos em din?mica n?o-linear sendo estudados com variantes deste circuito. Varreduras nos par?metros de controle podem fazer com que esse sistema oscile eletronicamente entre regi?es peri?dicas e regi?es ca?ticas. O diodo ? o elemento n?o linear respons?vel pelo surgimento do caos. Utilizando um modelo de capacit?ncia n?o linear para descrever o comportamento do diodo, podemos escrever as equa??es para esse sistema e estudar a sua din?mica numericamente. Nosso principal objetivo foi o estudo de expoentes cr?ticos complexos em bifurca??es din?micas. Para isso, realizamos um estudo num?rico do circuito RLD for?ado senoidalmente utilizando como par?metros de controle a frequ?ncia e a amplitude da tens?o de entrada. Constru?mos, a partir das s?ries temporais da corrente total e da tens?o no diodo, diagramas de bifurca??o com diferentes cortes estrobosc?picos, que apresentam cascata de dobramento de per?odo, janelas peri?dicas e transi??o intermitente. Tamb?m realizamos estudos num?ricos do comportamento da m?dia na regi?o de transi??o caos-peri?dico na busca de encontrar um expoente cr?tico caracter?stico e oscilas??es na m?dia, elementos que j? foram observados no mapa log?stico. N?o foram poss?veis observar numericamente as oscila??es, mas observamos um decaimento exponencial com expoente cr?tico de aproximadamente 0,5. Montamos um sistema de controle, aquisi??o e tratamento de dados experimentais no qual ? poss?vel a realiza??o remota de experimentos simult?neos com dois circuitos diferentes. Obtivemos diagramas de bifurca??es experimentais nos quais observamos que o sistema apresentahisterese e alta sensibilidade ?s condi??es do experimento como, por exemplo, o passo de varredura do par?metro de controle. / The RLD circuit, formed by a resistor, an inductor and a diode in series, displays a very rich dynamics when forced by an external harmonic voltage, and it has being studied for decades. However, there are some topics in nonlinear dynamics that are still studied with variants of this circuit nowadays. Changes in the control parameters may cause electronic oscillations between regular and chaotic regions.The diode is the nonlinear element responsible for the appearance of chaos. Using a nonlinear capacitance model to describe the behavior of the diode, we can write the equations for this system and study its dynamics numerically. Our main objective was the study of critical exponents in complex dynamic bifurcations. For that, we did a numerical study of the RLD circuit forced sinusoidally using as control parameters the amplitude of the input voltage and the frequency. We made, from the time series obtained, bifurcation diagrams with different stroboscopic cuts, which have cascade of period-doubling, periodic windows and intermittent transition. We also did numerical studies of the average behavior in the periodic-chaos transition region searching for characteristic critical exponent and oscilas??es on average, elements that have been observed in the logistic map. It was not possible to observe the oscillations numerically, but we observed an exponential decay with critical exponent of approximately 0.5. We set up a system able to control, acquire and process experimental data making it possible to perform remote simultaneous experiments with two different circuits. We have obtained experimental diagrams bifurcations in which we observe that the system has hysteresis and high sensitivity to the conditions of the experiment such as the step of scanning the control parameter.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/24397 |
| Date | 08 1900 |
| Creators | Onias, Heloisa Helena dos Santos |
| Contributors | Leite, Jos? Roberto Rios, Aguiar, Fl?vio Menezes de, Ori?, Marcos C?sar Santos, Leite, Jos? Roberto Rios |
| Publisher | Universidade Federal de Pernambuco, PROGRAMA DE P?S-GRADUA??O EM F?SICA, UFPE, Brasil, Departamento de F?sica |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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