91 resultados para Stable And Unstable Manifolds


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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Pós-graduação em Engenharia Elétrica - FEIS

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This work was developed from the study by Araujo, R.A.N. et al. Stability regions around the components of the triple system 2001 SN263. (Monthly Notices Of The Royal Astronomical Society, 2012, v. 423(4), 3058-3073 p.) where it was studied the stable and unstable regions system (2001 SN263), which is a triple asteroid system, and these are celestial orbiting our sun. Being close to the Earth is characterized as NEA (Near-Earth Asteroids), asteroids and which periodically approach the Earth's orbit, given that there is great interest in the study and exploitation of these objects, it is the key can carry features that contribute to better understand the process of formation of our solar system. Study the dynamics of bodies that govern those systems proves to be greatly attractive because of the mutual gravitational perturbation of bodies and also by external disturbances. Recently, NEA 2001 SN263 was chosen as a target of Aster mission where a probe is sent for this triple system, appearing therefore the need for obtaining information for characterizing stable regions internal and external to the system, with respect to the effects of radiation pressure. First, this study demonstrated that the integrator used showed satisfactory results of the orbital evolution of bodies in accordance with previous studies and also the characterization of stable and unstable regions brought similar results to the study by Araujo et al. (2012). From these results it was possible to carry out the implementation of the radiation pressure in the system in 2001 SN263, in a region close to the central body, where the simulations were carried out, which brought as a result that the regions before being characterized as stable in unstable true for small particles size from 1 to 5 micrometers. So the next orbital region to the central body and the ... ( Complete abstract click electronic access below)

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This work deals with the nonlinear piezoelectric coupling in vibration-based energy harvesting, done by A. Triplett and D.D. Quinn in J. of Intelligent Material Syst. and Structures (2009). In that paper the first order nonlinear fundamental equation has a three dimensional state variable. Introducing both observable and control variables in such a way the controlled system became a SISO system, we can obtain as a corollary that for a particular choice of the observable variable it is possible to present an explicit functional relation between this variable one, and the variable representing the charge harvested. After-by observing that the structure in the Input-Output decomposition essentially changes depending on the relative degree changes, presenting bifurcation branches in its zero dynamics-we are able in to identify this type of bifurcation indicating its close relation with the Hartman - Grobman theorem telling about decomposition into stable and the unstable manifolds for hyperbolic points.

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In this work we apply a nonperturbative approach to analyze soliton bifurcation ill the presence of surface tension, which is a reformulation of standard methods based on the reversibility properties of the system. The hypothesis is non-restrictive and the results can be extended to a much wider variety of systems. The usual idea of tracking intersections of unstable manifolds with some invariant set is again used, but reversibility plays an important role establishing in a geometrical point of view some kind of symmetry which, in a classical way, is unknown or nonexistent. Using a computer program we determine soliton solutions and also their bifurcations ill the space of parameters giving a picture of the chaotic structural distribution to phase and amplitude shift phenomena. (C) 2009 Published by Elsevier Ltd.

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We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.

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