Littérature scientifique sur le sujet « Unstable periodic orbits (UPOs) »
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Articles de revues sur le sujet "Unstable periodic orbits (UPOs)"
Saiki, Y., et M. Yamada. « Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems ». Nonlinear Processes in Geophysics 15, no 4 (7 août 2008) : 675–80. http://dx.doi.org/10.5194/npg-15-675-2008.
Texte intégralCOY, BENJAMIN. « DIMENSION REDUCTION FOR ANALYSIS OF UNSTABLE PERIODIC ORBITS USING LOCALLY LINEAR EMBEDDING ». International Journal of Bifurcation and Chaos 22, no 01 (janvier 2012) : 1230001. http://dx.doi.org/10.1142/s0218127412300017.
Texte intégralMorena, Matthew A., et Kevin M. Short. « Cupolets : History, Theory, and Applications ». Dynamics 4, no 2 (13 mai 2024) : 394–424. http://dx.doi.org/10.3390/dynamics4020022.
Texte intégralDolan, Kevin, Annette Witt, Jürgen Kurths et Frank Moss. « Spatiotemporal Distributions of Unstable Periodic Orbits in Noisy Coupled Chaotic Systems ». International Journal of Bifurcation and Chaos 13, no 09 (septembre 2003) : 2673–80. http://dx.doi.org/10.1142/s021812740300817x.
Texte intégralTIAN, YU-PING, et XINGHUO YU. « STABILIZING UNSTABLE PERIODIC ORBITS OF CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS ». International Journal of Bifurcation and Chaos 10, no 03 (mars 2000) : 611–20. http://dx.doi.org/10.1142/s0218127400000426.
Texte intégralBoukabou, A., A. Chebbah et A. Belmahboul. « Stabilizing Unstable Periodic Orbits of the Multi-Scroll Chua's Attractor ». Nonlinear Analysis : Modelling and Control 12, no 4 (25 octobre 2007) : 469–77. http://dx.doi.org/10.15388/na.2007.12.4.14678.
Texte intégralMaiocchi, Chiara Cecilia, Valerio Lucarini et Andrey Gritsun. « Decomposing the dynamics of the Lorenz 1963 model using unstable periodic orbits : Averages, transitions, and quasi-invariant sets ». Chaos : An Interdisciplinary Journal of Nonlinear Science 32, no 3 (mars 2022) : 033129. http://dx.doi.org/10.1063/5.0067673.
Texte intégralSaiki, Y. « Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors ». Nonlinear Processes in Geophysics 14, no 5 (14 septembre 2007) : 615–20. http://dx.doi.org/10.5194/npg-14-615-2007.
Texte intégralTIAN, YU-PING. « AN OPTIMIZATION APPROACH TO LOCATING AND STABILIZING UNSTABLE PERIODIC ORBITS OF CHAOTIC SYSTEMS ». International Journal of Bifurcation and Chaos 12, no 05 (mai 2002) : 1163–72. http://dx.doi.org/10.1142/s0218127402005017.
Texte intégralGritsun, A. « Statistical characteristics, circulation regimes and unstable periodic orbits of a barotropic atmospheric model ». Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences 371, no 1991 (28 mai 2013) : 20120336. http://dx.doi.org/10.1098/rsta.2012.0336.
Texte intégralThèses sur le sujet "Unstable periodic orbits (UPOs)"
Fazendeiro, L. A. M. « Unstable periodic orbits in turbulent hydrodynamics ». Thesis, University College London (University of London), 2011. http://discovery.ucl.ac.uk/1306183/.
Texte intégralPereira, Rodrigo Frehse. « Perturbações em sistemas com variabilidade da dimensão instável transversal ». UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2013. http://tede2.uepg.br/jspui/handle/prefix/902.
Texte intégralCoordenação de Aperfeiçoamento de Pessoal de Nível Superior
Unstable dimension variability (UDV) is an extreme form of nonhyperbolicity. It is a structurally stable phenomenon, typical for high dimensional chaotic systems, which implies severe restrictions to shadowing of perturbed solutions. Perturbations are unavoidable in modelling Physical phenomena, since no system can be made completely isolated, states and parameters cannot be determined without uncertainties and any numeric approach to such models is affected by truncation and/or roundoff errors. Thus, the lack of shadowability in systems exhibiting UDV presents a challenge for modelling. Aiming to unveil the effect of perturbations a class of nonhyperbolic systems is studied. These systems present transversal unstable dimension variability (TUDV), which means the dynamics can be split in a skew direct product form, i. e. the phase space is decomposed in two components: a hyperbolic chaotic one, called longitudinal, and a nonhyperbolic transversal one. Moreover, in the absence of perturbations, the longitudinal component is a global attractor of the system. A prototype composed of two coupled piecewise-linear chaotic maps is presented in order to study the TUDV effects. This system has an invariant subspace S which characterizes the complete chaos synchronization and UDV, when present, is transversal to it. Taking advantage of (piecewise) linearity of the equations, an analytical method for unstable periodic orbits’ computation is presented. The set of all unstable periodic orbits (UPOs) is one of the building block of chaotic dynamics and its properties provide valuable informations about the asymptotic behaviour of the system as, for instance, the invariant natural measure. Therefore, the TUDV’s intensity is analytically studied by computing the contrast measure, which quantifies the difference between the statistical weights associated to UPOs with different unstable dimension. The effect of perturbations is modelled by the introduction of a small parameter mismatch, instead of noise addition, in order to keep the model’s determinism. Consequently, the characterization of dynamics by means of UPOs is still possible. It is shown the existence of a dense set G of UPOs outside the invariant subspace consistent with a chaotic repeller. When perturbation takes place, G merges with the set H of UPOs previously in S, given rise to a new nonhyperbolic stationary state. The analysis of G ∪H provides a topological explanation to the behaviour of systems with TUDV under perturbations. Moreover, the relation between the set of UPOs embedded in a chaotic attractor and its natural measure, proven only for hyperbolic systems, is successfully applied to this system: the error between the natural measure estimated both numerically and by means of UPOs is shown to be decreasing with p, the considered UPOs’ period. It is conjectured the coincidence between both in limit. Hence, a positive answer to reliability of numerical estimation to natural measure in nonhyperbolic systems via unstable dimension variability is presented.
A variabilidade da dimensão instável (VDI) é uma forma extrema de não-hiperbolicidade. É um fenômeno estruturalmente estável, típico para sistemas caóticos de alta dimensionalidade, que implica restrições severas ao sombreamento de soluções perturbadas. As perturbações¸ s são inevitáveis na modelagem de fenômenos fíısicos, uma vez que nenhum sistema pode ser isolado completamente, os estados e os parâmetros não podem ser determinados sem incertezas e qualquer abordagem numérica dos modelos é afetada por erros de arredondamento e/ou truncamento. Portanto, a falta da sombreabilidade em sistemas exibindo VDI apresenta um desafio à modelagem. Visando revelar os efeitos das perturbações, uma classe desses sistemas não hiperbó licos é estudada. Esses sistemas apresentam variabilidade da dimensão instável transversal (VDIT), significando que a dinâmica pode ser decomposta na forma de um produto direto assimétrico, i. e. o espação de fase é dividido em dois componentes: um hiperbólico e caótico, dito longitudinal, e um transversal e não-hiperbólico. Mais ainda, na ausência de perturbações, o componente longitudinal é um atrator global do sistema. Um protótipo composto de dois mapas ca´oticos lineares por partes acoplados é apresentado para o estudo dos efeitos da VDIT. Esse sistema possui um subespaço invariante S que caracteriza a sincronização completa de caos e a VDI, quando presente, é transversal a esse subespaço. Valendo-se da linearidade (por partes) das equações, um método analítico para o cálculo das órbitas periódicas instáveis é apresentado. O conjunto de todas as órbitas periódicas instáveis (OPIs) é um dos fundamentos da dinâmica caótica e suas propriedades fornecem informaões, valiosas sobre o comportamento assintótico do sistema como, por exemplo, a medida natural invariante. Assim, a intensidade da VDIT é estudada analiticamente pelo cálculo da medida de contraste, que quantifica a diferença entre o peso estatístico associado às OPIs com dimensão instável distintas. O efeito das perturbações é modelado pela introdução de um pequeno desvio nos parâmetros, ao invés da adição de ruído, a fim de manter o determinismo do modelo. Consequentemente, a caracterização da dinâmica em termos das OPIs ainda é possível. Demonstra-se a existência de um conjunto denso G de OPIs fora do subespaço invariante consistente com um repulsor caótico. Na presença de perturbações, G se funde com o conjunto H das OPIs previamente em S, dando origem a um novo estado estacionario não-hiperbólico. A análise de G ∪H fornece uma explicação topológica ao comportamento de sistemas com variabilidade da dimensão instável sob a açãoo de perturbações. Mais ainda, a relação entre o conjunto de OPIs imersas em um atrator caótico e sua medida natural, provada apenas para sistemas hiperbólicos, é aplicada com sucesso nesse sistema: mostra-se que o erro entre as medidas naturais estimadas numericamente e pelas OPIs é decrescente com p, o período das OPIs consideradas. Conjectura-se, portanto, a coincidência entre ambas no limite . Logo, apresenta-se uma resposta positiva à estimativa numérica da medida natural em sistemas não-hiperbólicos via variabilidade da dimensão instável.
Chapitres de livres sur le sujet "Unstable periodic orbits (UPOs)"
Spano, M. L., W. L. Ditto, K. Dolan et F. Moss. « Unstable Periodic Orbits (UPOs) and Chaos Control in Neural Systems ». Dans Epilepsy as a Dynamic Disease, 297–322. Berlin, Heidelberg : Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05048-4_17.
Texte intégralMettin, R. « Entrainment Control of Chaos Near Unstable Periodic Orbits ». Dans Solid Mechanics and Its Applications, 231–38. Dordrecht : Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5778-0_29.
Texte intégralMoss, Frank E., et Hans A. Braun. « Unstable Periodic Orbits and Stochastic Synchronization in Sensory Biology ». Dans The Science of Disasters, 310–29. Berlin, Heidelberg : Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56257-0_10.
Texte intégralGrebogi, Celso, Edward Ott et James A. Yorke. « Unstable periodic orbits and the dimensions of multifractal chaotic attractors ». Dans The Theory of Chaotic Attractors, 335–48. New York, NY : Springer New York, 1988. http://dx.doi.org/10.1007/978-0-387-21830-4_19.
Texte intégralOtt, Edward, et Brian R. Hunt. « Control of Chaos by Means of Embedded Unstable Periodic Orbits ». Dans Control and Chaos, 134–41. Boston, MA : Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2446-4_8.
Texte intégralKawai, Yuki, et Tadashi Tsubone. « Stability Transformation Method for Unstable Periodic Orbits and Its Realization ». Dans Nonlinear Maps and their Applications, 109–19. New York, NY : Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-9161-3_11.
Texte intégralSmith, Leonard A. « Quantifying Chaos with Predictive Flows and Maps : Locating Unstable Periodic Orbits ». Dans NATO ASI Series, 359–66. Boston, MA : Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4757-0623-9_51.
Texte intégralIto, Daisuke, Tetsushi Ueta, Takuji Kousaka, Jun-ichi Imura et Kazuyuki Aihara. « Threshold Control for Stabilization of Unstable Periodic Orbits in Chaotic Hybrid Systems ». Dans Analysis and Control of Complex Dynamical Systems, 57–73. Tokyo : Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55013-6_6.
Texte intégralUeta, Tetsushi, Tohru Kawabe, Guanrong Chen et Hiroshi Kawakami. « Calculation and Control of Unstable Periodic Orbits in Piecewise Smooth Dynamical Systems ». Dans Chaos Control, 321–40. Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44986-7_14.
Texte intégralTian, Yu-Ping, et Xinghuo Yu. « Time-delayed Impulsive Stabilization of Unstable Periodic Orbits in Chaotic Hybrid Systems ». Dans Chaos Control, 51–69. Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44986-7_3.
Texte intégralActes de conférences sur le sujet "Unstable periodic orbits (UPOs)"
Sadeghian, Hoda, Kaveh Merat, Hassan Salarieh et Aria Alasty. « Chaos Control of a Sprott Circuit Using Non-Linear Delayed Feedback Control Via Sliding Mode ». Dans ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35020.
Texte intégralLiang, Yang, et B. F. Feeny. « Parametric Identification of Chaotic Systems Via a Long-Period Harmonic Balance ». Dans ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85032.
Texte intégralRahimi, Mohammad A., Hasan Salarieh et Aria Alasty. « Stabilizing Periodic Orbits of the Fractional Order Chaotic Van Der Pol System ». Dans ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40165.
Texte intégralSadeghian, Hoda, Mehdi Tabe Arjmand, Hassan Salarieh et Aria Alasty. « Chaos Control in Single Mode Approximation of T-AFM Systems Using Nonlinear Delayed Feedback Based on Sliding Mode Control ». Dans ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35018.
Texte intégralSadeghian, Hoda, Hassan Salarieh et Aria Alasty. « Chaos Control in Continuous Mode of T-AFM Systems Using Nonlinear Delayed Feedback via Sliding Mode Control ». Dans ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42794.
Texte intégralSieber, Jan, Bernd Krauskopf, David Wagg, Simon Neild et Alicia Gonzalez-Buelga. « Control-Based Continuation of Unstable Periodic Orbits ». Dans ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87007.
Texte intégralChakrabarty, Krishnendu, et Urmila Kar. « Stabilization of unstable periodic orbits in DC drives ». Dans 2015 International Conference on Electrical Engineering and Information Communication Technology (ICEEICT). IEEE, 2015. http://dx.doi.org/10.1109/iceeict.2015.7307356.
Texte intégralPen-Ning Yu, Min-Chi Hsiao, Dong Song, Charles Y. Liu, Christi N. Heck, David Millett et Theodore W. Berger. « Unstable periodic orbits in human epileptic hippocampal slices ». Dans 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE, 2014. http://dx.doi.org/10.1109/embc.2014.6944946.
Texte intégralAl-Zamel, Z., et B. F. Feeny. « Improved Estimations of Unstable Periodic Orbits Extracted From Chaotic Sets ». Dans ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21585.
Texte intégralCetinkaya, Ahmet, et Tomohisa Hayakawa. « Sampled-data delayed feedback control for stabilizing unstable periodic orbits ». Dans 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402408.
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