934 resultados para homoclinic chaos
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The background.--Economic chaos.--Reconstruction.
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Thesis (Master's)--University of Washington, 2016-06
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Thesis (Ph.D.)--University of Washington, 2016-06
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Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.
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The desire to know the future is as old as humanity. For the tourism industry the demand for accurate foretelling of the future course of events is a task that consumes considerable energy and is of great significance to investors. This paper examines the issue of forecasting by comparing forecasts of inbound tourism made prior to the political and economic crises that engulfed Indonesia from 1997 onwards with actual arrival figures. The paper finds that current methods of forecasting are not able to cope with unexpected crises and other disasters and that alternative methods need to be examined including scenarios, political risk and application of chaos theory. The paper outlines a framework for classifying shocks according to a scale of severity, probability, type of event, level of certainty and suggested forecasting tools for each scale of shock. (C) 2003 Elsevier Science Ltd. All rights reserved.
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The multibody dynamics of a satellite in circular orbit, modeled as a central body with two hinge-connected deployable solar panel arrays, is investigated. Typically, the solar panel arrays are deployed in orbit using preloaded torsional springs at the hinges in a near symmetrical accordion manner, to minimize the shock loads at the hinges. There are five degrees of freedom of the interconnected rigid bodies, composed of coupled attitude motions (pitch, yaw and roll) of the central body plus relative rotations of the solar panel arrays. The dynamical equations of motion of the satellite system are derived using Kane's equations. These are then used to investigate the dynamic behavior of the system during solar panel deployment via the 7-8th-order Runge-Kutta integration algorithms and results are compared with approximate analytical solutions. Chaotic attitude motions of the completely deployed satellite in circular orbit under the influence of the gravity-gradient torques are subsequently investigated analytically using Melnikov's method and confirmed via numerical integration. The Hamiltonian equations in terms of Deprit's variables are used to facilitate the analysis. (C) 2003 Published by Elsevier Ltd.
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How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.
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The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.
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Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.
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We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We de. ne a novel feature, Normalized Vector Separation (gamma(ij)), to measure the separation of two arbitrary states i and j in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that gamma(ij) can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via gamma(ij), with small NNs having no more than 21 connection weight altogether.
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Complex systems techniques provide a powerful tool to study the emergent properties of networks of interacting genes. In this study we extract models of genetic regulatory networks from an artificial genome, represented by a sequence of nucleotides, and analyse how variations in the connectivity and degree of inhibition of the extracted networks affects the resulting classes of behaviours. For low connectivity systems were found to be very stable. Only with higher connectivity was a significant occurrence of chaos found. Most interestingly, the peak in occurrence of chaos occurs perched on the edge of a phase transition in the occurrence of attractors.
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O Apocalipse de João é uma obra instigante. Sua linguagem cheia de violência, com monstros aterrorizantes, pessoas clamando por justiça, anúncios de mortes e desespero, em um quadro de espetáculos celestes, fascina os que gostam de ficção e alimenta a esperança dos que esperam um dia entrar na Nova Jerusalém, onde não haverá mar nem morte, quando as lágrimas serão enxugadas. Contudo, o livro do Apocalipse será lido como uma narração da realidade. Nesse sentido, o texto não é visto como reflexo de qualquer opressão, mas construção discursiva a respeito do sistema que, para o visionário, é a negação da ordem. Neste trabalho, a partir dos conceitos de texto e memória cultural, à luz das pesquisas de I. Lótman, da escola russa de semiótica da cultura e das pesquisas dos Assmann, observar-se-á como as memórias de seres celestes caídos e aprisionados da tradição enoquita estão presentes na literatura judaico-cristã e servem para a construção narrativa do cenário de terror escatológico na quinta e sexta trombetas de Ap 9,1-21. Assim sendo, a tese defende o terror como instrumento de persuasão, o qual serviu, na estratégia do visionário, para descrever o seu contexto como realidade caótica. Por meio de estratégias narrativas, o narrador deseja que sua visão seja levada a sério e que seus interlocutores aceitem a sua interpretação da realidade, deixando a associação com a vida e sistema romanos, pois se assim procederem serão comparados aos selados e receberão as mesmas recompensas. Dessa maneira, sua descrição com linguagem escatológica joga com o futuro e com o presente; prevê o caos, mas o vive em nível narrativo. Por isso o livro do Apocalipse, com um dualismo extremamente radical, não dá espaços para dúvidas. A tese defende, portanto, que essa obra pode ser lida como instrumento retórico de terror e medo que leva seus leitores implícitos a não flertarem com Roma, a não aceitarem seus discursos ou os que com ela se associam.
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Como estudar uma cultura ou uma comunidade perdida nos tempos bíblicos? Esta é um questão motriz para o autor. Foi dessa maneira que surgiu o seu interesse em discutir a possibilidade do uso do mito cosmogônico para o entendimento da comunidade dos cativos judaítas em Babilônia. É uma iniciativa, que precisava ser trilhada pelos pesquisadores que se dispusessem ao estudo das culturas do mundo bíblico. Assim se elegeu o tema Mito Cosmogônico no Primeiro Testamento como instrumento de aprofundamento da pesquisa bíblica. O mito é uma escolha mais ou menos óbvia, pela sua capacidade de funcionar como paradigma, pragmática e traditiva contra-hegemônica dentro de um contexto social interétnico. Estas eram ponderações vindas de matrizes como a do fenomenólogo Mircea Eliade, do Antropólogo Roger Bastide e do teólogo e fenomenólogo José Severino Croatto. É por isto que um paralelo é traçado entre o mito de Marduk e o texto de Isaías 51, 9-11, que fala de Javé como sendo criador do mundo e que luta contra as forças do caos. Isto é feito, com vistas à percepção da profecia do Isaías do exílio, como parentesco e sua justaposição com a mitologia babilônica, e ambos se aproximam bastante de forma sintagmática e histórico-social. Coube ainda saber se a profecia do Dêutero-Isaías atuava da mesma maneira que o poema Enuma elish funcionava para os babilônicos. Ou seja, fazia-se surgir modelos sociais às comunidades de escravos dentro do Império Neobabilônico; se com base nestes cânticos, os cativos conseguiam construir um ordenamento para as suas comunidades, que gozavam de uma relativa autonomia, tais como colônias e guetos ; se de posse dessa ousada profecia, os judeus da golah eram capazes de elaborar uma desobediência cívil nos termos de um nutrir nos corações, uma utopia que rompesse com o status quo do passado, comprometendo-os com a esperança no Javé criador.(AU)
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Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.