Synthesis of piece-wise linear functions and its application to chaotic oscillators

Although chaotic systems were first introduced to describe dynamical behaviors by modeling natural complex phenomena, they have been an important subject of research during the last two decades mainly because of the growing of the computing available resources. Nowadays, chaos research is present in...

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Detalhes bibliográficos
Autor: RODOLFO TREJO GUERRA
Tipo de documento: dissertação
Estado:Versión aceptada para publicación
Data de publicação:2008
País:México
Recursos:Instituto Nacional de Astrofísica, Óptica y Electrónica
Repositório:Repositorio Institucional del INAOE
Idioma:inglês
OAI Identifier:oai:inaoe.repositorioinstitucional.mx:1009/569
Acesso em linha:http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/569
Access Level:Acceso aberto
Palavra-chave:info:eu-repo/classification/Generadores de caos/Chaos generators
info:eu-repo/classification/Técnicas lineales por pieza/Piecewise linear techniques
info:eu-repo/classification/Generadores de funciones/Function generators
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/22
info:eu-repo/classification/cti/2203
info:eu-repo/classification/cti/330706
Descrição
Resumo:Although chaotic systems were first introduced to describe dynamical behaviors by modeling natural complex phenomena, they have been an important subject of research during the last two decades mainly because of the growing of the computing available resources. Nowadays, chaos research is present in very different fields to model complex behaviors such as: behavior of the human being, the market prices until physical relations between celestial corps, the modeling of fluids dynamics and information encrypting. As many phenomena in nature, most of the chaotic systems can be described and modeled by electrical circuits, which are then denoted as chaotic oscillators. There are several known forms to implement them, the majority of the electronic realizations are based on the use of operational amplifiers (Opamps) and in some cases, on more complex blocks like those which realize mathematical operations just as multiplication and division, with electrical signals mainly voltages. Among all the kinds of chaotic oscillators, there is a set which only requires differential operators and the use of destabilizing functions known as ”piece wise linear functions” or PWL functions. Such kinds of systems are among the simplest to be implemented by using electronic circuits; however, they are capable of achieving very complex dynamics. On the other hand, the implementation of PWL-based chaotic oscillators at the integrated circuit level, is becoming an important field of research. In this manner, this Thesis is devoted to implement such PWL-based chaotic systems using VLSI design techniques. The main contribution of this work is related to the use of unity-gain cells to build behavioral models and later to realize simulations using HSPICE and standard CMOS technology of 0.35μm. This implies for an analog circuit designer to take into account practical considerations with respect to the limited dynamical ranges, the system bandwidth and other characteristics analyzed in the singular blocks which conform the chaotic oscillator.