Propriedades dinâmicas e leis de escala em mapeamentos unidimensionais discretos: aplicações em circuitos

• Autor(a) principal: Ramos, Larissa Cristina Nascimento
• Data de Publicação: 2019
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/217136
• topic: Circuitos elétricos; Comportamento caótico nos sistemas; Sistemas não lineares; Telecomunicações

In this work some dynamic properties will be investigated in the Smith and Slatkin map parameterized by the γ exponent and the control parameters α and r. This mapping belongs to a set of discrete one-dimensional maps used to describe the dynamics of biological populations. Nonlinear dynamic systems can be described by mappings that depend on control parameters. Thus, if the control parameters change, the system may exhibit different behaviors. Initially, the bifurcation diagram was numerically build to illustrate the behavior of the dynamic system, so the stability and the chaos could be observed. The Lyapunov exponents were used to characterize the chaos in the system. After that a small parametric perturbation defined by the control parameters ε and bn was introduced in the system and changes could be observed in the bifurcation diagram. Our studies was extended in the investigation of parameter space. The investigation of parameter space in one-dimensional maps is a current scientific theme, little known in the literature and requires a great computational effort. Using the calculation of Lyapunov exponents, we build the parameter spaces for the Smith and Slatkin map in order to explore the structures known as shrimps. This knowledge was applied to the study of the chaotic circuit of Chua.