Готові списки джерел за темами / Chaotic behavior in systems

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Добірка наукової літератури з теми "Chaotic behavior in systems"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 29 липня 2024

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Статті в журналах з теми "Chaotic behavior in systems"

HOLDEN, ARUN V., and MAX J. LAB. "Chaotic Behavior in Excitable Systems." Annals of the New York Academy of Sciences 591, no. 1 Mathematical (June 1990): 303–15. http://dx.doi.org/10.1111/j.1749-6632.1990.tb15097.x.

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Alfaro, Miguel D., and Juan M. Sepulveda. "Chaotic behavior in manufacturing systems." International Journal of Production Economics 101, no. 1 (May 2006): 150–58. http://dx.doi.org/10.1016/j.ijpe.2005.05.012.

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Wu, Xiaomao, and Z. A. Schelly. "Chaotic behavior of chemical systems." Reaction Kinetics and Catalysis Letters 42, no. 2 (September 1990): 303–7. http://dx.doi.org/10.1007/bf02065364.

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Wang, Tianyi. "Classification of Chaotic Behaviors in Jerky Dynamical Systems." Complex Systems 30, no. 1 (February 15, 2021): 93–110. http://dx.doi.org/10.25088/complexsystems.30.1.93.

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Differential equations are widely used to model systems that change over time, some of which exhibit chaotic behaviors. This paper proposes two new methods to classify these behaviors that are utilized by a supervised machine learning algorithm. Dissipative chaotic systems, in contrast to conservative chaotic systems, seem to follow a certain visual pattern. Also, the machine learning program written in the Wolfram Language is utilized to classify chaotic behavior with an accuracy around 99.1±1.1%.

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YANG, XIAO-SONG, and LEI WANG. "EMERGENT PERIODIC BEHAVIOR IN COUPLED CHAOTIC SYSTEMS." Advances in Complex Systems 09, no. 03 (September 2006): 249–61. http://dx.doi.org/10.1142/s0219525906000793.

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Emergent behavior in interconnected systems (complex systems) is of fundamental significance in natural and engineering sciences. A commonly investigated problem is how complicated dynamics take place in dynamical systems consisting of (often simple) subsystems. It is shown though numerical experiments that emergent order such as periodic behavior can likely take place in coupled chaotic dynamical systems. This is demonstrated for the particular case of coupled chaotic continuous time Hopfield neural networks. In particular, it is shown that when two chaotic Hopfield neural networks are coupled by simple sigmoid signals, periodic behavior can emerge as a consequence of this coupling.

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VIANA, R. L., S. E. DE S. PINTO, J. R. R. BARBOSA, and C. GREBOGI. "PSEUDO-DETERMINISTIC CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 13, no. 11 (November 2003): 3235–53. http://dx.doi.org/10.1142/s0218127403008636.

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We call a chaotic dynamical system pseudo-deterministic when it does not produce numerical, or pseudo-trajectories that stay close, or shadow chaotic true trajectories, even though the model equations are strictly deterministic. In this case, single chaotic trajectories may not be meaningful, and only statistical predictions, at best, could be drawn on the model, like in a stochastic system. The dynamical reason for this behavior is nonhyperbolicity characterized either by tangencies of stable and unstable manifolds or by the presence of periodic orbits embedded in a chaotic invariant set with a different number of unstable directions. We emphasize herewith the latter by studying a low-dimensional discrete-time model in which the phenomenon appears due to a saddle-repeller bifurcation. We also investigate the behavior of the finite-time Lyapunov exponents for the system, which quantifies this type of nonhyperbolicity as a system parameter evolves past a critical value. We argue that the effect of unstable dimension variability is more intense when the invariant chaotic set of the system loses transversal stability through a blowout bifurcation.

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Dewangan, Omprakash. "Machine Learning Approaches for Predicting Chaotic Behavior in Nonlinear Systems." Communications on Applied Nonlinear Analysis 30, no. 3 (December 27, 2023): 01–15. http://dx.doi.org/10.52783/cana.v30.275.

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In many domains, including biology, engineering, physics, and finance, the ability to forecast chaotic behavior is of the utmost importance. Predicting nonlinear systems accurately is a critical task due to their intrinsic sensitivity to initial conditions and lack of apparent patterns. One potential way to address this difficulty is by utilizing machine learning techniques. These methods can help us better understand and manage complex systems that display chaotic dynamics. Complex nonlinear systems, with their great dimensionality, temporal interdependence, and sensitivity to initial conditions, make chaotic behavior prediction difficult. The development of sophisticated tools that can detect patterns in chaotic dynamics is often necessary because traditional methods fail to capture these subtleties. The present research presents Chaotic Dynamics Prediction through Deep Ensemble Learning (CDP-DEL), an approach to chaotic dynamics prediction (CDP) that combines deep learning architectures with ensemble learning methodologies. Ensemble learning improves generalizability and reduces overfitting, whereas deep neural networks are made to capture complicated nonlinear interactions. CDP-DEL is an all-inclusive method for predicting chaotic behavior in nonlinear systems since it uses feature engineering, integrates system factors, and handles temporal dependencies. Among the many fields that have found use for CDP-DEL are control systems, ecological research, financial modeling, and weather forecasting. When applied to real-world scenarios with substantial chaotic dynamics repercussions, CDP-DEL's improved prediction capabilities may help optimize decision-making processes. Extensive simulation evaluations are performed utilizing benchmark chaotic systems to validate the efficacy of CDP-DEL. Research comparing CDP-DEL to more conventional methods show that it is more effective at predicting chaotic behavior and overall outperforms the competition.

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Wang, Z., S. Panahi, A. J. M. Khalaf, S. Jafari, and I. Hussain. "Synchronization of chaotic jerk systems." International Journal of Modern Physics B 34, no. 20 (August 5, 2020): 2050189. http://dx.doi.org/10.1142/s0217979220501891.

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Chaotic jerk oscillators belong to the simplest chaotic systems. These systems try to model the behavior of dynamical systems efficiently. Jerk oscillators can be known as the most general systems in science, especially physics. It has been proved that every dynamical system expressed with an ordinary differential equation is able to describe as a jerky system in particular conditions. One of its main topics is investigating the collective behavior of chaotic jerk oscillators in the dynamical network. In this paper, the synchronizability of the identical network of jerk oscillators is examined in three different coupling configurations, which are velocity, acceleration, and jerk coupling, and the results are compared with each other.

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Alessio, Francesca, Vittorio Coti Zelati, and Piero Montecchiari. "Chaotic behavior of rapidly oscillating Lagrangian systems." Discrete & Continuous Dynamical Systems - A 10, no. 3 (2004): 687–707. http://dx.doi.org/10.3934/dcds.2004.10.687.

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Zielinska, Barbara J. A., David Mukamel, Victor Steinberg, and Shmuel Fishman. "Chaotic behavior in externally modulated hydrodynamic systems." Physical Review A 32, no. 1 (July 1, 1985): 702–5. http://dx.doi.org/10.1103/physreva.32.702.

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Дисертації з теми "Chaotic behavior in systems"

Michaels, Alan Jason. "Digital chaotic communications." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/34849.

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This dissertation provides the conceptual development, modeling and simulation, physical implementation, and measured hardware results for a practicable digital coherent chaotic communication system. Such systems are highly desirable for robust communications due to the maximal entropy signal characteristics that satisfy Shannon's ideal noise-like waveform and provide optimal data transmission across a flat communications channel. At the core of the coherent chaotic communications system is a fully digital chaotic circuit, providing an efficiently controllable mechanism that overcomes the traditional bottleneck of chaotic circuit state synchronization. The analytical, simulation, and hardware results yield a generalization of direct sequence spread spectrum waveforms, that can be further extended to create a new class of maximal entropy waveforms suitable for optimized channel performance, maximal entropy transmission of chaotically spread amplitude modulated data constellations, and permission-based multiple access systems.

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Çek, Mehmet Emre Savacı Ferit Acar. "Analysis of observed chaotic data/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/elektronikvehaberlesme/T000493.rar.

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Çiftçi, Mahmut. "Channel equalization for chaotic communications systems." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/15464.

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Carlu, Mallory. "Instability in high-dimensional chaotic systems." Thesis, University of Aberdeen, 2019. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=240675.

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Анотація:

In this thesis I make extensive use of the Lyapunov analysis formalism to unravel fundamental mechanisms of instability in two diﬀerent systems : the Kuramoto model of globally coupled phase-oscillators and the Lorenz 96 (L96) atmospheric "toy" model, portraying the evolution of a physical quantity along a latitude circle. I start by introducing the relevant theoretical background, with special attention on the main tools I have been using throughout this work : Lyapunov Exponents (LEs), which quantify the asymptotic growth rates of inﬁnitesimal perturbations in a system, and by extension, its degree of chaoticity, and Covariant Lyapunov Vectors (CLVs), which indicate the phase space direction (or the geometry) associated with these growth rates. The Kuramoto model is central in the study of synchronization among oscillatory units characterized by their various natural frequencies, but little is known on its chaotic dynamics in the unsynchronized state. I thus investigate the scaling behavior of the ﬁrst LE, upon diﬀerent assumptions on the natural frequencies, and make use of educated structural simpliﬁcations to analyze the origin of chaos in the ﬁnite size model. On the other hand, the L96 model has been devised to gather the main dynamical ingredients of atmospheric dynamics, namely advection, damping, external (solar) forcing and transfers across diﬀerent scales of motion, in a minimalist and functional way. It features two coupled dynamical layers : the large scale variables, representing synoptic scale atmospheric dynamics, and the small scale variables, faster and more numerous, associated with convective scale dynamics. The core of the study revolves around geometrical properties of CLVs, in the aim of understanding the processes underlying the observed multiscale chaoticity, and an exhaustive study of a non-trivial ensemble of CLVs featuring relevant projection on the slow subspace.

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Reiss, Joshua D. "The analysis of chaotic time series." Diss., Full text available online (restricted access), 2001. http://images.lib.monash.edu.au/ts/theses/reiss.pdf.

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Ghofranih, Jahangir. "Control and estimation of a chaotic system." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29601.

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A class of deterministic nonlinear systems known as ”chaotic” behaves similar to noise-corrupted systems. As a specific example, Duffing equation, a nonlinear oscillator representing the roll dynamics of a vessel, was chosen for the study. State estimation and control of such systems in the presence of measurement noise is the prime goal of this research. A nonlinear estimation suitable for chaotic systems was evaluated against conventional methods based on linear equivalent model, and proved to be very efficient. A state feedback controller and a sliding mode controller were applied to the chaotic system and both techniques provided satisfactory results. Investigating the persistence of chaotic behavior of the controlled system is a secondary goal. Simulation results showed that the chaotic behavior persisted in case of the linear feedback controller, while in case of the sliding mode controller the system did not exhibit any chaotic behavior.
Applied Science, Faculty of
Electrical and Computer Engineering, Department of
Graduate

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Cromwell, Jeff B. "Chaotic price dynamics of agricultural commodities." Morgantown, W. Va. : [West Virginia University Libraries], 2004. https://etd.wvu.edu/etd/controller.jsp?moduleName=documentdata&jsp%5FetdId=3625.

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Thesis (Ph. D.)--West Virginia University, 2004.
Title from document title page. Document formatted into pages; contains vi, 166 p. : ill. Includes abstract. Includes bibliographical references (p. 142-160).

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Lindquist, Roslyn Gay. "The dimension of a chaotic attractor." PDXScholar, 1991. https://pdxscholar.library.pdx.edu/open_access_etds/4182.

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Tools to explore chaos are as far away as a personal computer or a pocket calculator. A few lines of simple equations in BASIC produce fantastic graphic displays. In the following computer experiment, the dimension of a strange attractor is found by three algorithms; Shaw's, Grassberger-Procaccia's and Guckenheimer's. The programs were tested on the Henon attractor which has a known fractal dimension. Shaw's and Guckenheimer's algorithms were tested with 1000 data points, and Grassberger's with 100 points, a data set easily handled by a PC in one hour or less using BASIC or any other language restricted to 640K RAM. Since dimension estimates are notorious for requiring many data points, the author wanted to find an algorithm to quickly estimate a low-dimensional system (around 2). Although all three programs gave results in the neighborhood of the fractal dimension for the Henon attractor, Dfracta1=1.26, none appeared to converge to the fractal dimension.

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Fleming-Dahl, Arthur. "A chaotic communication system with a receiver estimation engine." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15651.

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Akguc, Gursoy Bozkurt. "Chaos in 2D electron waveguides." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts Internaional, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3035928.

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Книги з теми "Chaotic behavior in systems"

Casati, Giulio, ed. Chaotic Behavior in Quantum Systems. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-2443-0.

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Marek, Miloš. Chaotic behaviour of deterministic dissipative systems. Cambridge: Cambridge University Press, 1991.

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Marek, Miloš. Chaotic Behaviour of Deterministic Dissipative Systems. Cambridge [England]: Cambridge University Press, 1991.

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Gitterman, M. The chaotic pendulum. New Jersey: World Scientific, 2010.

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Fabio, Casciati, ed. Dynamic motion, chaotic and stochastic behaviour. Austria: Springer-Verlag, 1994.

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1948-, Hsu Sze-Bi, ed. Lectures on chaotic dynamical systems. Providence, R.I: American Mathematical Society, 2003.

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Hoppensteadt, F. C. Analysis and simulation of chaotic systems. New York: Springer-Verlag, 1993.

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Wiggins, Stephen. Chaotic transport in dynamical systems. New York: Springer-Verlag, 1992.

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Baker, Gregory L. Chaotic dynamics: An introduction. 2nd ed. Cambridge: Cambridge University Press, 1996.

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1944-, Gollub J. P., ed. Chaotic dynamics: An introduction. Cambridge [England]: Cambridge University Press, 1990.

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Частини книг з теми "Chaotic behavior in systems"

Hanias, M. P., H. E. Nistazakis, and G. S. Tombras. "Chaotic Behavior of Transistor Circuits." In Understanding Complex Systems, 59–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29329-0_4.

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Cervelle, Julien, Alberto Dennunzio, and Enrico Formenti. "Chaotic Behavior of Cellular Automata." In Encyclopedia of Complexity and Systems Science, 1–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-642-27737-5_65-4.

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Cervelle, Julien, Alberto Dennunzio, and Enrico Formenti. "Chaotic Behavior of Cellular Automata." In Encyclopedia of Complexity and Systems Science, 978–89. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-30440-3_65.

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Meyer, H. D. "Chaotic Behavior of Classical Hamiltonian Systems." In Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics, 143–57. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3005-6_10.

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Krabs, Werner, and Stefan Pickl. "Chaotic Behavior of Autonomous Time-Discrete Systems." In Dynamical Systems, 149–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13722-8_3.

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Josiński, Henryk, Agnieszka Michalczuk, Adam Świtoński, Romualda Mucha, and Konrad Wojciechowski. "Quantifying Chaotic Behavior in Treadmill Walking." In Intelligent Information and Database Systems, 317–26. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15705-4_31.

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Wisniewski, Helena S. "Bounds for the Chaotic Behavior of Newton’s Method." In Dynamics of Infinite Dimensional Systems, 481–510. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-86458-2_39.

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Nishimura, Jun, and Tomohisa Hayakawa. "Chaotic Behavior of Orthogonally Projective Triangle Folding Map." In Analysis and Control of Complex Dynamical Systems, 77–90. Tokyo: Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55013-6_7.

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Hacinliyan, Avadis Simon, Orhan Ozgur Aybar, Ilknur Kusbeyzi Aybar, Mustafa Kulali, and Seyma Karaduman. "Signals of Chaotic Behavior in Middle Eastern Stock Exchanges." In Chaos and Complex Systems, 353–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33914-1_48.

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Biswas, Debabrata, and Tanmoy Banerjee. "Collective Behavior-I: Synchronization in Hyperchaotic Time-Delayed Oscillators Coupled Through a Common Environment." In Time-Delayed Chaotic Dynamical Systems, 57–78. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70993-2_4.

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Тези доповідей конференцій з теми "Chaotic behavior in systems"

Gómez, J. M. G., L. Muñoz, J. Retamosa, R. A. Molina, A. Relaño, and E. Faleiro. "Chaotic Behavior of Nuclear Systems." In Proceedings of the Predeal International Summer School in Nuclear Physics. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770417_0008.

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C. de Queiroz, Fernando, Tiago Pereira, Eddie Nijholt, and Dmitry Turaev. "Chaotic Behavior in Diffusively Coupled Systems." In v. 10 n. 1 (2023): CNMAC 2023. SBMAC, 2023. http://dx.doi.org/10.5540/03.2023.010.01.0002.

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Ikeda, Hideo. "Chaotic behavior in complex shop scheduling." In 2012 Joint 6th Intl. Conference on Soft Computing and Intelligent Systems (SCIS) and 13th Intl. Symposium on Advanced Intelligent Systems (ISIS). IEEE, 2012. http://dx.doi.org/10.1109/scis-isis.2012.6505303.

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Uppal, J. S., Weiping Lu, A. Johnstone, and R. G. Harrison. "Generic Chaotic Behavior of Stimulated Brillouin Scattering." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.oc558.

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We report first evidence of chaotic emission in stimulated Brillouin scattering under cw pump conditions involving a single Stoke and pump signal. Single mode optical fibre is used as the nonlinear medium. First analysis of this fundamental process establishes chaotic dynamics to be prevalent in both the Stokes and transmitted pump signals; existing over a very wide parameter region including that close to the SBS threshold. The interplay of nonlinear dispersion with Brillouin gain is identified as a key mechanism responsible for this behaviour.

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Graham, R. "Quantized Chaotic Systems." In Instabilities and Dynamics of Lasers and Nonlinear Optical Systems. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/idlnos.1985.thc1.

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Chaos is a typical form of dynamical behavior of classical nonlinear dynamical systems. In conservative Hamiltonian systems with f degrees of freedom chaos appears if the system is not intergrable and in some regions of phase space trajectories are not restricted to f-dimensional smooth manifolds. In dissipative systems chaos in the dynamical steady state appears if the system has a strange attractor in configuration space.

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Evans, Allan K. "The long-time behavior of correlation functions in dynamical systems." In Stochastic and chaotic dynamics in the lakes. AIP, 2000. http://dx.doi.org/10.1063/1.1302412.

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Gu, Pengyun, Steven Dubowsky, and Constantinos Mavroidis. "The Design Implications of Chaotic and Near-Chaotic Vibrations in Machines." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5849.

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Abstract Accurate performance prediction is key to the design of high performance machines. It is shown here that connection clearance and component flexibility can result in machine dynamic behaviors that are hypersensitive to small variations of system design parameters and operating conditions. These hypersensitivities, which can limit the usefulness of computer dynamic simulations for design, are associated with chaotic and near chaotic behavior. The dynamic behaviors of two systems, an Impact Beam System and a Spatial Slider Crank, are studied. The chaotic vibration of these systems is confirmed numerically and experimentally. Hypersensitivity is shown for both chaotic and periodic response regions, in which case actual dynamic behavior of such machines could be very different in practice from that predicated by design simulation studies. Design guidelines are developed for evaluating the fatigue life and the reliability of machines under these conditions.

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Goldman, Paul, and Agnes Muszynska. "Chaotic Behavior of Rotor/Stator Systems With Rubs." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-387.

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This paper outlines the dynamic behavior of externally excited rotor/stator systems with occasional, partial rubbing conditions. The observed phenomenon have one major source of a strong nonlinearity: transition from no contact to contact state between mechanical elements, one of which is rotating. This results in variable stiffness and damping, impacting, and intermittent involvement of friction. A new model for such a transition (impact) is developed. In case of the contact between rotating and stationary elements, it correlates the local radial and tangential (“super ball”) effects with global behavior of the system. The results of numerical simulations of a simple rotor/stator system based on that model are presented in the form of bifurcation diagrams, rotor lateral vibration time–base waves, and orbits. The vibrational behavior of the considered system is characterized by orderly harmonic and subharmonic responses, as well as by chaotic vibrations. A new result (additional subharmonic regime of vibration) is obtained for the case of heavy rub of an anisotropically supported rotor. The correspondence between numerical simulation and previously obtained experimental data supports the adequacy of the new model of impact.

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Kaloutsakis, G. "Chaotic Behavior of a Self-Replicating Robotic Population." In Topics on Chaotic Systems - Selected Papers from CHAOS 2008 International Conference. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814271349_0020.

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Cull, P. "Linear Fractionals - Simple Models with Chaotic-like Behavior." In COMPUTING ANTICIPATORY SYSTEMS: CASYS 2001 - Fifth International Conference. AIP, 2002. http://dx.doi.org/10.1063/1.1503683.

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Звіти організацій з теми "Chaotic behavior in systems"

Narducci, L. M. Instabilities and Chaotic Behavior of Active and Passive Laser Systems. Fort Belvoir, VA: Defense Technical Information Center, March 1985. http://dx.doi.org/10.21236/ada153366.

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Bodruzzaman, M., and M. A. Essawy. Chaotic behavior control in fluidized bed systems using artificial neural network. Quarterly progress report, October 1, 1996--December 31, 1996. Office of Scientific and Technical Information (OSTI), February 1996. http://dx.doi.org/10.2172/493394.

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Bodruzzaman, M., and M. A. Essawy. Chaotic behavior control in fluidized bed systems using artificial neural network. Quarterly progress report, April 1, 1996--June 30, 1996. Office of Scientific and Technical Information (OSTI), July 1996. http://dx.doi.org/10.2172/410400.

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Soloviev, Vladimir, Andrii Bielinskyi, Oleksandr Serdyuk, Victoria Solovieva, and Serhiy Semerikov. Lyapunov Exponents as Indicators of the Stock Market Crashes. [б. в.], November 2020. http://dx.doi.org/10.31812/123456789/4131.

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Анотація:

The frequent financial critical states that occur in our world, during many centuries have attracted scientists from different areas. The impact of similar fluctuations continues to have a huge impact on the world economy, causing instability in it concerning normal and natural disturbances [1]. The an- ticipation, prediction, and identification of such phenomena remain a huge chal- lenge. To be able to prevent such critical events, we focus our research on the chaotic properties of the stock market indices. During the discussion of the re- cent papers that have been devoted to the chaotic behavior and complexity in the financial system, we find that the Largest Lyapunov exponent and the spec- trum of Lyapunov exponents can be evaluated to determine whether the system is completely deterministic, or chaotic. Accordingly, we give a theoretical background on the method for Lyapunov exponents estimation, specifically, we followed the methods proposed by J. P. Eckmann and Sano-Sawada to compute the spectrum of Lyapunov exponents. With Rosenstein’s algorithm, we com- pute only the Largest (Maximal) Lyapunov exponents from an experimental time series, and we consider one of the measures from recurrence quantification analysis that in a similar way as the Largest Lyapunov exponent detects highly non-monotonic behavior. Along with the theoretical material, we present the empirical results which evidence that chaos theory and theory of complexity have a powerful toolkit for construction of indicators-precursors of crisis events in financial markets.

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Bodruzzaman, M. Chaotic behavior monitoring & control in fluidized bed systems using artificial neural network. Quarterly progress report, July 1, 1996--September 30, 1996. Office of Scientific and Technical Information (OSTI), October 1996. http://dx.doi.org/10.2172/477756.

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Jen, E., M. Alber, R. Camassa, W. Choi, J. Crutchfield, D. Holm, G. Kovacic, and J. Marsden. Applied mathematics of chaotic systems. Office of Scientific and Technical Information (OSTI), July 1996. http://dx.doi.org/10.2172/257451.

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Wang, Hua O., and Eyad H. Abed. Bifurcation Control of Chaotic Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, June 1992. http://dx.doi.org/10.21236/ada454958.

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Collins, Lee A., and Christopher Ticknor. Chaotic Behavior: Bose-Einstein Condensate in a Disordered Potential. Office of Scientific and Technical Information (OSTI), April 2014. http://dx.doi.org/10.2172/1129053.

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Abarbanel, H. D. Topics in Pattern Formation and Chaotic Systems. Fort Belvoir, VA: Defense Technical Information Center, May 1993. http://dx.doi.org/10.21236/ada265922.

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Geller, Jil T., Sharon E. Borglin, and Boris A. Faybishenko. Experiments and evaluation of chaotic behavior of dripping waterin fracture models. Office of Scientific and Technical Information (OSTI), June 2001. http://dx.doi.org/10.2172/900684.

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