Relevant bibliographies by topics / Unstable periodic orbits (UPOs)

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Unstable periodic orbits (UPOs)'

Author: Grafiati
Published: 22 July 2024
Last updated: 31 July 2025

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Journal articles on the topic "Unstable periodic orbits (UPOs)"

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Saiki, Y., and M. Yamada. "Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems." Nonlinear Processes in Geophysics 15, no. 4 (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, no. 01 (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 t
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Morena, Matthew A., and Kevin M. Short. "Cupolets: History, Theory, and Applications." Dynamics 4, no. 2 (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, unstabl
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Dolan, Kevin, Annette Witt, Jürgen Kurths, and Frank Moss. "Spatiotemporal Distributions of Unstable Periodic Orbits in Noisy Coupled Chaotic Systems." International Journal of Bifurcation and Chaos 13, no. 09 (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
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TIAN, YU-PING, and XINGHUO YU. "STABILIZING UNSTABLE PERIODIC ORBITS OF CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS." International Journal of Bifurcation and Chaos 10, no. 03 (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 shal
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Boukabou, A., A. Chebbah, and A. Belmahboul. "Stabilizing Unstable Periodic Orbits of the Multi-Scroll Chua's Attractor." Nonlinear Analysis: Modelling and Control 12, no. 4 (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, and 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 (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 approxim
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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, no. 5 (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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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, no. 1991 (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
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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, no. 05 (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
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Dissertations / Theses on the topic "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 flu
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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<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>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 compl
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(10329018), Yanxing Song. "Developing new methods for chaos control and synchronization." Thesis, 2002. https://figshare.com/articles/thesis/Developing_new_methods_for_chaos_control_and_synchronization/26343826.

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<p dir="ltr">The aim of this research is to develop new techniques on chaos control and synchronization. One difference between chaos control and the traditional control is that in traditional control the reference signal is explicitly expressed, which is available directly; and in chaos control, in many cases, the reference signal is one of its unstable periodic orbits (UPOs), which needs to work out with methods such as delay coordinate embedding technique or to be replaced by the historical data as the analytic expression of the signal cannot be obtained directly (more details can be found
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Books on the topic "Unstable periodic orbits (UPOs)"

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Coveney, Peter V., and Shunzhou Wan. Molecular Dynamics: Probability and Uncertainty. Oxford University PressOxford, 2025. https://doi.org/10.1093/9780198893479.001.0001.

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Abstract This book explores the intersection of molecular dynamics (MD) simulation with advanced probabilistic methodologies to address the inherent uncertainties in the approach. Beginning with a clear and comprehensible introduction to classical mechanics, the book transitions into the probabilistic formulation of MD, highlighting the importance of ergodic theory, kinetic theory, and unstable periodic orbits, concepts which are largely unknown to current practitioners within the domain. It discussed ensemble-based simulations, free energy calculations and the study of polymer nanocomposites
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Book chapters on the topic "Unstable periodic orbits (UPOs)"

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Spano, M. L., W. L. Ditto, K. Dolan, and F. Moss. "Unstable Periodic Orbits (UPOs) and Chaos Control in Neural Systems." In Epilepsy as a Dynamic Disease. 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." In Solid Mechanics and Its Applications. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5778-0_29.

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

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Grebogi, Celso, Edward Ott, and James A. Yorke. "Unstable periodic orbits and the dimensions of multifractal chaotic attractors." In The Theory of Chaotic Attractors. Springer New York, 1988. http://dx.doi.org/10.1007/978-0-387-21830-4_19.

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

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Kawai, Yuki, and Tadashi Tsubone. "Stability Transformation Method for Unstable Periodic Orbits and Its Realization." In Nonlinear Maps and their Applications. 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." In NATO ASI Series. 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, and Kazuyuki Aihara. "Threshold Control for Stabilization of Unstable Periodic Orbits in Chaotic Hybrid Systems." In Analysis and Control of Complex Dynamical Systems. 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, and Hiroshi Kawakami. "Calculation and Control of Unstable Periodic Orbits in Piecewise Smooth Dynamical Systems." In Chaos Control. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44986-7_14.

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

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Conference papers on the topic "Unstable periodic orbits (UPOs)"

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Tavasoli, Ali, and Heman Shakeri. "Operator-Based Detecting, Learning, and Stabilizing Unstable Periodic Orbits of Chaotic Attractors." In 2024 American Control Conference (ACC). IEEE, 2024. http://dx.doi.org/10.23919/acc60939.2024.10644947.

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Sadeghian, Hoda, Kaveh Merat, Hassan Salarieh, and Aria Alasty. "Chaos Control of a Sprott Circuit Using Non-Linear Delayed Feedback Control Via Sliding Mode." In 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 st
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Liang, Yang, and B. F. Feeny. "Parametric Identification of Chaotic Systems Via a Long-Period Harmonic Balance." In 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, and Aria Alasty. "Stabilizing Periodic Orbits of the Fractional Order Chaotic Van Der Pol System." In 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 demonstratio
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Sadeghian, Hoda, Mehdi Tabe Arjmand, Hassan Salarieh, and Aria Alasty. "Chaos Control in Single Mode Approximation of T-AFM Systems Using Nonlinear Delayed Feedback Based on Sliding Mode Control." In 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 presen
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Sadeghian, Hoda, Hassan Salarieh, and Aria Alasty. "Chaos Control in Continuous Mode of T-AFM Systems Using Nonlinear Delayed Feedback via Sliding Mode Control." In 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 P
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Sieber, Jan, Bernd Krauskopf, David Wagg, Simon Neild, and Alicia Gonzalez-Buelga. "Control-Based Continuation of Unstable Periodic Orbits." In 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 f
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Chakrabarty, Krishnendu, and Urmila Kar. "Stabilization of unstable periodic orbits in DC drives." In 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, et al. "Unstable periodic orbits in human epileptic hippocampal slices." In 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., and B. F. Feeny. "Improved Estimations of Unstable Periodic Orbits Extracted From Chaotic Sets." In 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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