Bibliografías temáticas / Unstable periodic orbits (UPOs)

Literatura académica sobre el tema "Unstable periodic orbits (UPOs)"

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Publicado: 22 de julio de 2024

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Artículos de revistas sobre el tema "Unstable periodic orbits (UPOs)"

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Saiki, Y. y M. Yamada. "Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems". Nonlinear Processes in Geophysics 15, n.º 4 (7 de agosto de 2008): 675–80. http://dx.doi.org/10.5194/npg-15-675-2008.

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Abstract. Unstable periodic orbit (UPO) recently has become a keyword in analyzing complex phenomena in geophysical fluid dynamics and space physics. In this paper, sets of UPOs in low dimensional maps are theoretically or systematically found, and time averaged properties along UPOs are studied, in relation to those of chaotic orbits.
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COY, BENJAMIN. "DIMENSION REDUCTION FOR ANALYSIS OF UNSTABLE PERIODIC ORBITS USING LOCALLY LINEAR EMBEDDING". International Journal of Bifurcation and Chaos 22, n.º 01 (enero de 2012): 1230001. http://dx.doi.org/10.1142/s0218127412300017.

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An autonomous four-dimensional dynamical system is investigated through a topological analysis. This system generates a chaotic attractor for the range of control parameters studied and we determine the organization of the unstable periodic orbits (UPOs) associated with the chaotic attractor. Surrogate UPOs were found in the four-dimensional phase space and pairs of these orbits were embedded in three-dimensions using Locally Linear Embedding. This is a dimensionality reduction technique recently developed in the machine learning community. Embedding pairs of orbits allows the computation of their linking numbers, a topological invariant. A table of linking numbers was computed for a range of control parameter values which shows that the organization of the UPOs is consistent with that of a Lorenz-type branched manifold with rotation symmetry.
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Morena, Matthew A. y Kevin M. Short. "Cupolets: History, Theory, and Applications". Dynamics 4, n.º 2 (13 de mayo de 2024): 394–424. http://dx.doi.org/10.3390/dynamics4020022.

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In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to form the skeleton of the associated attractors. While UPOs are insightful tools for analysis, they are naturally unstable and, as such, are difficult to find and computationally expensive to stabilize. An alternative to using UPOs is to approximate them using cupolets. Cupolets, a name derived from chaotic, unstable, periodic, orbit-lets, are a relatively new class of waveforms that represent highly accurate approximations to the UPOs of chaotic systems, but which are generated via a particular control scheme that applies tiny perturbations along Poincaré sections. Originally discovered in an application of secure chaotic communications, cupolets have since gone on to play pivotal roles in a number of theoretical and practical applications. These developments include using cupolets as wavelets for image compression, targeting in dynamical systems, a chaotic analog to quantum entanglement, an abstract reducibility classification, a basis for audio and video compression, and, most recently, their detection in a chaotic neuron model. This review will detail the historical development of cupolets, how they are generated, and their successful integration into theoretical and computational science and will also identify some unanswered questions and future directions for this work.
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Dolan, Kevin, Annette Witt, Jürgen Kurths y Frank Moss. "Spatiotemporal Distributions of Unstable Periodic Orbits in Noisy Coupled Chaotic Systems". International Journal of Bifurcation and Chaos 13, n.º 09 (septiembre de 2003): 2673–80. http://dx.doi.org/10.1142/s021812740300817x.

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Techniques for detecting encounters with unstable periodic orbits (UPOs) have been very successful in the analysis of noisy, experimental time series. We present here a technique for applying the topological recurrence method of UPO detection to spatially extended systems. This approach is tested on a network of diffusively coupled chaotic Rössler systems, with both symmetric and asymmetric coupling schemes. We demonstrate how to extract encounters with UPOs from such data, and present a preliminary method for analyzing the results and extracting dynamical information from the data, based on a linear correlation analysis of the spatiotemporal occurrence of encounters with these low period UPOs. This analysis can provide an insight into the coupling structure of such a spatially extended system.
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TIAN, YU-PING y XINGHUO YU. "STABILIZING UNSTABLE PERIODIC ORBITS OF CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS". International Journal of Bifurcation and Chaos 10, n.º 03 (marzo de 2000): 611–20. http://dx.doi.org/10.1142/s0218127400000426.

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A novel adaptive time-delayed control method is proposed for stabilizing inherent unstable periodic orbits (UPOs) in chaotic systems with unknown parameters. We first explore the inherent properties of chaotic systems and use the system state and time-delayed system state to form an asymptotically stable invariant manifold so that when the system state enters the manifold and stays in it thereafter, the resulting motion enables the stabilization of the desired UPOs. We then use the model following concept to construct an identifier for the estimation of the uncertain system parameters. We shall prove that under the developed scheme, the system parameter estimates will converge to their true values. The effectiveness of the method is confirmed by computer simulations.
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Boukabou, A., A. Chebbah y A. Belmahboul. "Stabilizing Unstable Periodic Orbits of the Multi-Scroll Chua's Attractor". Nonlinear Analysis: Modelling and Control 12, n.º 4 (25 de octubre de 2007): 469–77. http://dx.doi.org/10.15388/na.2007.12.4.14678.

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This paper addresses the control of the n-scroll Chua’s circuit. It will be shown how chaotic systems with multiple unstable periodic orbits (UPOs) detected in the Poincar´e section can be stabilized as well as taking the system dynamics from one UPO to another.
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Maiocchi, Chiara Cecilia, Valerio Lucarini y 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, n.º 3 (marzo de 2022): 033129. http://dx.doi.org/10.1063/5.0067673.

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Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems, as they allow one to distill their dynamical structure. We consider here the Lorenz 1963 model with the classic parameters’ value. We investigate how a chaotic trajectory can be approximated using a complete set of UPOs up to symbolic dynamics’ period 14. At each instant, we rank the UPOs according to their proximity to the position of the orbit in the phase space. We study this process from two different perspectives. First, we find that longer period UPOs overwhelmingly provide the best local approximation to the trajectory. Second, we construct a finite-state Markov chain by studying the scattering of the orbit between the neighborhood of the various UPOs. Each UPO and its neighborhood are taken as a possible state of the system. Through the analysis of the subdominant eigenvectors of the corresponding stochastic matrix, we provide a different interpretation of the mixing processes occurring in the system by taking advantage of the concept of quasi-invariant sets.
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Saiki, Y. "Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors". Nonlinear Processes in Geophysics 14, n.º 5 (14 de septiembre de 2007): 615–20. http://dx.doi.org/10.5194/npg-14-615-2007.

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Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.
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TIAN, YU-PING. "AN OPTIMIZATION APPROACH TO LOCATING AND STABILIZING UNSTABLE PERIODIC ORBITS OF CHAOTIC SYSTEMS". International Journal of Bifurcation and Chaos 12, n.º 05 (mayo de 2002): 1163–72. http://dx.doi.org/10.1142/s0218127402005017.

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In this paper, a novel method for locating and stabilizing inherent unstable periodic orbits (UPOs) in chaotic systems is proposed. The main idea of the method is to formulate the UPO locating problem as an optimization issue by using some inherent properties of UPOs of chaotic systems. The global optimal solution of this problem yields the desired UPO. To avoid a local optimal solution, the state of the controlled chaotic system is absorbed into the initial condition of the optimization problem. The ergodicity of chaotic dynamics guarantees that the optimization process does not stay forever at any local optimal solution. When the chaotic orbit approaches the global optimal solution, which is the desired UPO, the controller will stabilize it at the UPO, and the optimization process will cease simultaneously. The method has been developed for both discrete-time and continuous-time systems, and validated for some typical chaotic systems such as the Hénon map and the Duffing oscillator, among others.
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Gritsun, 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, n.º 1991 (28 de mayo de 2013): 20120336. http://dx.doi.org/10.1098/rsta.2012.0336.

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The theory of chaotic dynamical systems gives many tools that can be used in climate studies. The widely used ones are the Lyapunov exponents, the Kolmogorov entropy and the attractor dimension characterizing global quantities of a system. Another potentially useful tool from dynamical system theory arises from the fact that the local analysis of a system probability distribution function (PDF) can be accomplished by using a procedure that involves an expansion in terms of unstable periodic orbits (UPOs). The system measure (or its statistical characteristics) is approximated as a weighted sum over the orbits. The weights are inversely proportional to the orbit instability characteristics so that the least unstable orbits make larger contributions to the PDF. Consequently, one can expect some relationship between the least unstable orbits and the local maxima of the system PDF. As a result, the most probable system trajectories (or ‘circulation regimes’ in some sense) may be explained in terms of orbits. For the special classes of chaotic dynamical systems, there is a strict theory guaranteeing the accuracy of this approach. However, a typical atmospheric model may not qualify for these theorems. In our study, we will try to apply the idea of UPO expansion to the simple atmospheric system based on the barotropic vorticity equation of the sphere. We will check how well orbits approximate the system attractor, its statistical characteristics and PDF. The connection of the most probable states of the system with the least unstable periodic orbits will also be analysed.
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Tesis sobre el tema "Unstable periodic orbits (UPOs)"

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Fazendeiro, L. A. M. "Unstable periodic orbits in turbulent hydrodynamics". Thesis, University College London (University of London), 2011. http://discovery.ucl.ac.uk/1306183/.

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In this work we describe a novel parallel space-time algorithm for the computation of periodic solutions of the driven, incompressible Navier-Stokes equations in the turbulent regime. Efforts to apply the machinery of dynamical systems theory to fluid turbulence depend on the ability to accurately and reliably compute such unstable periodic orbits (UPOs). These UPOs can be used to construct the dynamical zeta function of the system, from which very accurate turbulent averages of observables can be extracted from first principles, thus circumventing the inherently statistical description of fluid turbulence. In order to identify these orbits we use a space-time variational principle, first introduced in 2004. This approach has not, to the best of our knowledge, been used before on dynamical systems of high dimension because of the formidable storage and computation required. In this thesis we describe the utilization of petascale high performance computation to the problem of applying this space-time algorithm to hydrodynamic turbulence. The lattice-Boltzmann method is used to simulate the Navier-Stokes equations, due to its locality, and is implemented in a fully-parallel software package using the Message Passing Interface. This implementation, called HYPO4D, was successfully deployed on a large variety of platforms both in the UK and the US with an extremely good scalability to tens of thousands of computing cores. Based on this fluid solver other routines were developed, for the systematic location of suitable candidate spacetime minima and their numerical relaxation, using the gradient descent and conjugate gradient algorithms. Following this methodology, several UPOs are identified in homogeneous turbulence driven by an Arnold-Beltrami-Childress force field in three spatial dimensions, at Reynolds numbers corresponding to weakly-turbulent flow. We characterize the transition to turbulence in the ABC flow and the periodic orbits computed, for a flow with Re = 371, after the transients have died down. The work concludes with a discussion of the potential for this approach to become a new paradigm in the study of driven dissipative dynamical systems.
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Pereira, 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.

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Made available in DSpace on 2017-07-21T19:26:04Z (GMT). No. of bitstreams: 1 Rodrigo Frehse Pereira.pdf: 4666622 bytes, checksum: b2dcf2959eef9f7fd82301c2e45ac87f (MD5) Previous issue date: 2013-03-01
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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.
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Capítulos de libros sobre el tema "Unstable periodic orbits (UPOs)"

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Spano, M. L., W. L. Ditto, K. Dolan y F. Moss. "Unstable Periodic Orbits (UPOs) and Chaos Control in Neural Systems". En 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.

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Mettin, R. "Entrainment Control of Chaos Near Unstable Periodic Orbits". En Solid Mechanics and Its Applications, 231–38. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5778-0_29.

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Moss, Frank E. y Hans A. Braun. "Unstable Periodic Orbits and Stochastic Synchronization in Sensory Biology". En The Science of Disasters, 310–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56257-0_10.

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Grebogi, Celso, Edward Ott y James A. Yorke. "Unstable periodic orbits and the dimensions of multifractal chaotic attractors". En 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.

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Ott, Edward y Brian R. Hunt. "Control of Chaos by Means of Embedded Unstable Periodic Orbits". En Control and Chaos, 134–41. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2446-4_8.

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Kawai, Yuki y Tadashi Tsubone. "Stability Transformation Method for Unstable Periodic Orbits and Its Realization". En 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.

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Smith, Leonard A. "Quantifying Chaos with Predictive Flows and Maps: Locating Unstable Periodic Orbits". En NATO ASI Series, 359–66. Boston, MA: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4757-0623-9_51.

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Ito, Daisuke, Tetsushi Ueta, Takuji Kousaka, Jun-ichi Imura y Kazuyuki Aihara. "Threshold Control for Stabilization of Unstable Periodic Orbits in Chaotic Hybrid Systems". En 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.

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Ueta, Tetsushi, Tohru Kawabe, Guanrong Chen y Hiroshi Kawakami. "Calculation and Control of Unstable Periodic Orbits in Piecewise Smooth Dynamical Systems". En Chaos Control, 321–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44986-7_14.

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Tian, Yu-Ping y Xinghuo Yu. "Time-delayed Impulsive Stabilization of Unstable Periodic Orbits in Chaotic Hybrid Systems". En Chaos Control, 51–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44986-7_3.

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Actas de conferencias sobre el tema "Unstable periodic orbits (UPOs)"

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Sadeghian, Hoda, Kaveh Merat, Hassan Salarieh y Aria Alasty. "Chaos Control of a Sprott Circuit Using Non-Linear Delayed Feedback Control Via Sliding Mode". En ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35020.

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In this paper a nonlinear delayed feedback control is proposed to control chaos in a nonlinear electrical circuit which is known as Sprott circuit. The chaotic behavior of the system is suppressed by stabilizing one of its first order Unstable Periodic Orbits (UPOs). Firstly, the system parameters assumed to be known, and a nonlinear delayed feedback control is designed to stabilize the UPO of the system. Then the sliding mode scheme of the proposed controller is presented in presence of model parameter uncertainties. The effectiveness of the presented methods is numerically investigated by stabilizing the unstable first order periodic orbit and is compared with a typical linear delayed feedback control. Simulation results show the high performance of the methods for chaos elimination in Sprott circuit.
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Liang, Yang y B. F. Feeny. "Parametric Identification of Chaotic Systems Via a Long-Period Harmonic Balance". En ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85032.

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Hyperbolic chaotic sets are composed of a countable infinity of unstable periodic orbits (UPOs). Symbol dynamics reveals that any long chaotic segment can be approximated by a UPO, which is a periodic solution to an ideal model of the system. Treated as such, the harmonic balance method is applied to the long chaotic segments to identify model parameters. Ultimately, this becomes a frequency domain identification method applied to chaotic systems.
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Rahimi, Mohammad A., Hasan Salarieh y Aria Alasty. "Stabilizing Periodic Orbits of the Fractional Order Chaotic Van Der Pol System". En ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40165.

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In this paper, stabilizing the unstable periodic orbits (UPO) in a chaotic fractional order system called Van der Pol is studied. Firstly, a technique for finding unstable periodic orbit in chaotic fractional order systems is stated. Then by applying this technique to the van der Pol system, unstable periodic orbit of system is found. After that, a method is presented for stabilization of the discovered UPO based on theories stability of the linear integer order and fractional order systems. Finally, a linear feedback controller was applied to the system and simulation is done for demonstration of controller performance.
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Sadeghian, Hoda, Mehdi Tabe Arjmand, Hassan Salarieh y Aria Alasty. "Chaos Control in Single Mode Approximation of T-AFM Systems Using Nonlinear Delayed Feedback Based on Sliding Mode Control". En ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35018.

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The taping mode Atomic Force Microscopic (T-AFM) can be properly described by a sinusoidal excitation of its base and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In this paper a nonlinear delayed feedback control is proposed to control chaos in a single mode approximation of a T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback control. The effectiveness of the presented methods is numerically verified and the results show the high performance of the controller.
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Sadeghian, Hoda, Hassan Salarieh y Aria Alasty. "Chaos Control in Continuous Mode of T-AFM Systems Using Nonlinear Delayed Feedback via Sliding Mode Control". En ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42794.

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The taping mode Atomic Force Microscopic (T-AFM) can be assumed as a cantilever beam which its base is excited by a sinusoidal force and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In order to modeling, using the galerkin method, the PDE equation is reduced to a single ODE equation which properly describing the continuous beam. In this paper a nonlinear delayed feedback control is proposed to control chaos in T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback control. The numerical results show the high quality and good performance of the proposed method.
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Sieber, Jan, Bernd Krauskopf, David Wagg, Simon Neild y Alicia Gonzalez-Buelga. "Control-Based Continuation of Unstable Periodic Orbits". En ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87007.

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We present an experimental procedure to track periodic orbits through a fold (saddle-node) bifurcation, and demonstrate it with a parametrically excited pendulum experiment where the control parameter is the amplitude of the excitation. Specifically, we track the initially stable period-one rotation of the pendulum through its fold bifurcation and along the unstable branch. The fold bifurcation itself corresponds physically to the minimal amplitude that is able to support sustained rotation. Our scheme is based on a modification of time-delayed feedback in a continuation setting, and we show for an idealized model that it converges with the same efficiency as classical proportional-plus-derivative control.
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Chakrabarty, Krishnendu y Urmila Kar. "Stabilization of unstable periodic orbits in DC drives". En 2015 International Conference on Electrical Engineering and Information Communication Technology (ICEEICT). IEEE, 2015. http://dx.doi.org/10.1109/iceeict.2015.7307356.

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Pen-Ning Yu, Min-Chi Hsiao, Dong Song, Charles Y. Liu, Christi N. Heck, David Millett y Theodore W. Berger. "Unstable periodic orbits in human epileptic hippocampal slices". En 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.

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Al-Zamel, Z. y B. F. Feeny. "Improved Estimations of Unstable Periodic Orbits Extracted From Chaotic Sets". En 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.

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Abstract Unstable periodic orbits of the saddle type are often extracted from chaotic sets. We use the recurrence method of extracting segments of the chaotic data to approximate the true unstable periodic orbit. Then nearby trajectories are then examined to obtain the dynamics local to the extracted orbit, in terms of an affine map. The affine map is then used to estimate the true orbit. Accuracy is evaluated in examples including well known maps and the Duffing oscillator.
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Cetinkaya, Ahmet y Tomohisa Hayakawa. "Sampled-data delayed feedback control for stabilizing unstable periodic orbits". En 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402408.

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