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Master's Dissertation
DOI
10.11606/D.55.2008.tde-01072008-164134
Document
Author
Full name
Wescley Bonomo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2008
Supervisor
Committee
Rodrigues, Hildebrando Munhoz (President)
Ruas Filho, Jose Gaspar
Santos, Jair Silverio dos
Title in Portuguese
Sistemas dinâmicos discretos: estabilidade, comportamento assintótico e sincronização
Keywords in Portuguese
Atrator de Lorenz
Comportamento assintótico
Equações de diferenças finitas
Estabilidade e instabilidade
Método direto de Liapunov
Sincronização
Sistemas dinâmicos discretos
Sistemas lineares de equações de diferenças
Abstract in Portuguese
Este trabalho é em parte baseado no livro The Stability and Control of Discrete Processes de Joseph P. LaSalle. Nós estudamos equações como x(n+1) = T(x(n)), onde T : ' R POT. m' ' SETA' 'R POT. m' é uma aplicação contínua, com o sistema dinâmico associado 'PI' (n,x) := ' T POT. n' (x). Nós fornecemos condições suficientes para a estabilidade de equilíbrios usando o método direto de Liapunov. Também consideramos sistemas discretos da forma x(n+1)=T(n, x(n),'lâmbda' ) dependendo de uma parâmetro ' lâmbda' e apresentamos resultados obtendo estimativas de atratores. Finalmente, nós apresentamos algumas simulações de sistemas acoplados como uma aplicação em sistemas de comunicação
Title in English
Discrete dynamical systems: stability, asymptotic behavior and synchronization
Keywords in English
Asymptotic behavior
Discrete dynamical systems
Finite difference equations
Liapunov's direct method
Linear systems of difference equations
Lorenz' s attractor
Stability and instability
Synchronization
Abstract in English
This work is in part based on the book The Stability and Control of Discrete Processes of Joseph P. LaSalle. We studing equations as x(n+1) = T(x(n)), where T : ' R POT.m' ' ARROW' ' ' R POT.m' is continuous transformation, with the associated dynamic system 'PI' (n,x) := ' T POT.n' (x). We provide suddicient conditions for stability of equilibria, using Liapunov direct method. We also consider nonautonomous discrete systems of the form x(n + 1) = T(n, x(n), ' lâmbda') depending on the parameter 'lâmbda' and present results obtaining uniform estimatives of attractors. We finally we present some simulations on synchronization of coupled systems as an application on communication systems
 
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wescley.pdf (1.57 Mbytes)
Publishing Date
2008-07-01
 
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