Relevant bibliographies by topics / Nonlinear periodic systems

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

Academic literature on the topic 'Nonlinear periodic systems'

Author: Grafiati
Published: 19 October 2024
Last updated: 31 July 2025

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Journal articles on the topic "Nonlinear periodic systems"

1

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Nonlinear Multivalued Periodic Systems." Journal of Dynamical and Control Systems 25, no. 2 (2018): 219–43. http://dx.doi.org/10.1007/s10883-018-9408-9.

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Luo, Albert C. J. "Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems." International Journal of Bifurcation and Chaos 25, no. 03 (2015): 1550044. http://dx.doi.org/10.1142/s0218127415500443.

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This paper presents a semi-analytical method for periodic flows in continuous nonlinear dynamical systems. For the semi-analytical approach, differential equations of nonlinear dynamical systems are discretized to obtain implicit maps, and a mapping structure based on the implicit maps is employed for a periodic flow. From mapping structures, periodic flows in nonlinear dynamical systems are predicted analytically and the corresponding stability and bifurcations of the periodic flows are determined through the eigenvalue analysis. The periodic flows predicted by the single-step implicit maps a
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Verriest, Erik I. "Balancing for Discrete Periodic Nonlinear Systems." IFAC Proceedings Volumes 34, no. 12 (2001): 249–54. http://dx.doi.org/10.1016/s1474-6670(17)34093-4.

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Sundararajan, P., and S. T. Noah. "Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems." Journal of Vibration and Acoustics 119, no. 1 (1997): 9–20. http://dx.doi.org/10.1115/1.2889694.

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The analysis of systems subjected to periodic excitations can be highly complex in the presence of strong nonlinearities. Nonlinear systems exhibit a variety of dynamic behavior that includes periodic, almost-periodic (quasi-periodic), and chaotic motions. This paper describes a computational algorithm based on the shooting method that calculates the periodic responses of a nonlinear system under periodic excitation. The current algorithm calculates also the stability of periodic solutions and locates system parameter ranges where aperiodic and chaotic responses bifurcate from the periodic res
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Can, Le Xuan. "On periodic waves of the nonlinear systems." Vietnam Journal of Mechanics 20, no. 4 (1998): 11–19. http://dx.doi.org/10.15625/0866-7136/10037.

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The paper is concerned with the solvability and approximate solution of the nonlinear partial differential equation describing the periodic wave propagation. Necessary and sufficient conditions for the existence of the periodic wave solutions are obtained. An approximate method for solving the equation is presented. As an illustrative example, the equation of periodic waves of the electric cables is considered.
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Ortega, Juan-Pablo. "Relative normal modes for nonlinear Hamiltonian systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 3 (2003): 665–704. http://dx.doi.org/10.1017/s0308210500002602.

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An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits in the energy levels surrounding a stable equilibrium. The estimate obtained is very precise in the sense that it provides a lower bound for the number of relative periodic orbits at each prescribed energy and momentum values neighbouring the stable relative equilibrium in questi
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Grigoraş, Victor, and Carmen Grigoraş. "Connecting Analog and Discrete Nonlinear Systems for Noise Generation." Bulletin of the Polytechnic Institute of Iași. Electrical Engineering, Power Engineering, Electronics Section 68, no. 1 (2022): 81–90. http://dx.doi.org/10.2478/bipie-2022-0005.

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Abstract Nonlinear systems exhibit complex dynamic behaviour, including quasi-periodic and chaotic. The present contribution presents a composed analogue and discrete-time structure, based on second-order nonlinear building blocks with periodic oscillatory behaviour, that can be used for complex signal generation. The chosen feedback connection of the two modules aims at obtaining a more complex nonlinear dynamic behaviour than that of the building blocks. Performing a parameter scan, it is highlighted that the resulting nonlinear system has a quasi-periodic behaviour for large ranges of param
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Zhang, Yu, Xue Yang, and Yong Li. "Affine-Periodic Solutions for Dissipative Systems." Abstract and Applied Analysis 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/157140.

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As generalizations of Yoshizawa’s theorem, it is proved that a dissipative affine-periodic system admits affine-periodic solutions. This result reveals some oscillation mechanism in nonlinear systems.
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Abbas, Saïd, Mouffak Benchohra, Soufyane Bouriah, and Juan J. Nieto. "Periodic solutions for nonlinear fractional differential systems." Differential Equations & Applications, no. 3 (2018): 299–316. http://dx.doi.org/10.7153/dea-2018-10-21.

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Kamenskii, Mikhail, Oleg Makarenkov, and Paolo Nistri. "Small parameter perturbations of nonlinear periodic systems." Nonlinearity 17, no. 1 (2003): 193–205. http://dx.doi.org/10.1088/0951-7715/17/1/012.

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Dissertations / Theses on the topic "Nonlinear periodic systems"

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Tang, Xiafei. "Periodic disturbance rejection of nonlinear systems." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/periodic-disturbance-rejection-of-nonlinear-systems(0bddefd9-2750-47fd-8c92-c90a01b8e1ef).html.

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Disturbance rejection is an important topic in control design since disturbances are inevitable in practical systems. To realise this target for nonlinear systems, this thesis brings in an assumption about the existence of a controlled invariant mani- fold and a Desired Feedforward Control (DFC) which is contained in the input to compensate the influence of disturbances. According to the approximation property of Neural Networks (NN) that any periodic signals defined in a compact set can be approximated by NN, the NN-based disturbance approximator is applied to approximate the DFC. Algorithmic
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Abd-Elrady, Emad. "Nonlinear Approaches to Periodic Signal Modeling." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4644.

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Groves, James O. "Small signal analysis of nonlinear systems with periodic operating trajectories." Diss., This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-06062008-162614/.

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Zhang, Zhen. "Adaptive robust periodic output regulation." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1187118803.

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Khames, Imene. "Nonlinear network wave equations : periodic solutions and graph characterizations." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR04/document.

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Dans cette thèse, nous étudions les équations d’ondes non-linéaires discrètes dans des réseaux finis arbitraires. C’est un modèle général, où le Laplacien continu est remplacé par le Laplacien de graphe. Nous considérons une telle équation d’onde avec une non-linéarité cubique sur les nœuds du graphe, qui est le modèle φ4 discret, décrivant un réseau mécanique d’oscillateurs non-linéaires couplés ou un réseau électrique où les composantes sont des diodes ou des jonctions Josephson. L’équation d’onde linéaire est bien comprise en termes de modes normaux, ce sont des solutions périodiques associ
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Warkomski, Edward Joseph 1958. "Nonlinear structures subject to periodic and random vibration with applications to optical systems." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/277811.

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The methods for analysis of a three degree-of-freedom nonlinear optical support system, subject to periodic and random vibration, are presented. The analysis models were taken from those generated for the dynamic problems related to the NASA Space Infrared Telescope Facility (SIRTF). The models treat the one meter, 116 kilogram (258 pound) primary mirror of the SIRTF as a rigid mass, with elastic elements representing the mirror support structure. Both linear and nonlinear elastic supports are evaluated for the SIRTF. Advanced Continuous Simulation Language (ACSL), a commercially available sof
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Zhang, Xiaohong. "Optimal feedback control for nonlinear discrete systems and applications to optimal control of nonlinear periodic ordinary differential equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40185.

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Myers, Owen Dale. "Spatiotemporally Periodic Driven System with Long-Range Interactions." ScholarWorks @ UVM, 2015. http://scholarworks.uvm.edu/graddis/524.

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It is well known that some driven systems undergo transitions when a system parameter is changed adiabatically around a critical value. This transition can be the result of a fundamental change in the structure of the phase space, called a bifurcation. Most of these transitions are well classified in the theory of bifurcations. Among the driven systems, spatiotemporally periodic (STP) potentials are noteworthy due to the intimate coupling between their time and spatial components. A paradigmatic example of such a system is the Kapitza pendulum, which is a pendulum with an oscillating suspensio
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Hayward, Peter J. "On the computation of periodic responses for nonlinear dynamic systems with multi-harmonic forcing." Thesis, University of Sussex, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.429733.

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Royston, Thomas James. "Computational and Experimental Analyses of Passive and Active, Nonlinear Vibration Mounting Systems Under Periodic Excitation /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487928649987553.

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Books on the topic "Nonlinear periodic systems"

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Reithmeier, Eduard. Periodic Solutions of Nonlinear Dynamical Systems. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0094521.

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Chulaevskiĭ, V. A. Almost periodic operators and related nonlinear integrable systems. Manchester University Press, 1989.

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Ambrosetti, A. Periodic solutions of singular Lagrangian systems. Birkhäuser, 1993.

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author, Bolle Philippe, ed. Quasi-periodic solutions of nonlinear wave equations in the D-dimensional torus. European Mathematical Society, 2020.

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Reithmeier, Eduard. Periodic solutions of nonlinear dynamical systems: Numerical computation, stability, bifurcation, and transition to chaos. Springer-Verlag, 1991.

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P, Walker K., and United States. National Aeronautics and Space Administration., eds. Nonlinear mesomechanics of composites with periodic microstructure: Final report on NASA NAG3-882. National Aeronautics and Space Administration, 1991.

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Fiedler, Bernold. Global bifurcation of periodic solutions with symmetry. Springer-Verlag, 1988.

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Luo, Albert C. J. Periodic Flows to Chaos in Time-delay Systems. Springer, 2016.

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Chulaevsky, V. A. Almost Periodic Operators and Related Nonlinear Integrable Systems (Nonlinear Science: Theory & Application). John Wiley & Sons, 1992.

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Coti-Zelati, V., and A. Ambrosetti. Periodic Solutions of Singular Lagrangian Systems. Birkhauser Verlag, 2012.

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Book chapters on the topic "Nonlinear periodic systems"

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Toda, Morikazu. "Periodic Systems." In Theory of Nonlinear Lattices. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83219-2_4.

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Luo, Albert C. J. "Periodic Flows in Continuous Systems." In Nonlinear Physical Science. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47275-0_5.

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Szemplińska-Stupnicka, Wanda. "Secondary Resonances (Periodic and Almost-Periodic)." In The Behavior of Nonlinear Vibrating Systems. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1870-2_7.

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Akhmet, Marat. "Discontinuous Almost Periodic Functions." In Nonlinear Systems and Complexity. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20572-0_3.

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Akhmet, Marat. "Discontinuous Almost Periodic Solutions." In Nonlinear Systems and Complexity. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20572-0_4.

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Anishchenko, Vadim S., Tatyana E. Vadivasova, and Galina I. Strelkova. "Synchronization of Periodic Self-Sustained Oscillations." In Deterministic Nonlinear Systems. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06871-8_13.

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Belyakov, Vladimir Alekseevich. "Nonlinear Optics of Periodic Media." In Partially Ordered Systems. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4396-0_6.

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Akhmet, Marat. "Periodic Solutions of Nonlinear Systems." In Principles of Discontinuous Dynamical Systems. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6581-3_7.

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Luo, Albert C. J. "Periodic Flows in Time-delay Systems." In Nonlinear Systems and Complexity. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42778-2_4.

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Luo, Albert C. J. "Periodic Flows in Time-Delay Systems." In Nonlinear Systems and Complexity. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42664-8_3.

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Conference papers on the topic "Nonlinear periodic systems"

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Sukhorukov, Andrey A., N. Marsal, A. Minovich, et al. "Control of modulational instability in periodic feedback systems." In Nonlinear Photonics. OSA, 2010. http://dx.doi.org/10.1364/np.2010.nmd7.

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Shermeneva, Maria. "Nonlinear periodic waves on a slope." In Modeling complex systems. AIP, 2001. http://dx.doi.org/10.1063/1.1386843.

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Vakakis, Alexander. "Nonlinear Periodic Systems: Bands and Localization." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87315.

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We consider the dynamics of nonlinear mono-coupled periodic media. When coupling dominates over nonlinearity near-field standing waves and spatially extended traveling waves exist, inside stop and pass bands, respectively, of the nonlinear system. Nonlinear standing waves are analytically studied using a nonlinear normal mode formulation, whereas nonlinear traveling waves are analyzed by the method of multiple scales. When the nonlinear effects are of the same order with the coupling ones a completely different picture emerges, since nonlinear resonance interactions are unavoidable. As a resul
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Vladimirov, A. G., E. B. Pelyukhova, and E. E. Fradkin. "Periodic and Chaotic Operations of a Laser with a Saturable Absorber." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.oc527.

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We study numerically and analytically the small amplitude periodic solutions of semiclassical equations for a laser with a saturable absorber. We investigate the bifurcation sequence, leading to period-doublings, crises of chaotic attractors, and intermittency.
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Mandel, Paul, N. P. Pettiaux, Wang Kaige, P. Galatola, and L. A. Lugiato. "Generic Properties of Periodic Attractors in Two-Photon Processes." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.ob257.

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We show that the periodic attractors occurring in two-photon processes displaying a phase instability have common properties including a domain of hysteresis. The case of degenerate four-wave mixing includes also some nongeneric attractors which exhibit a Berry phase phenomenon.
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Winful, Herbert G., Shawe-Shiuan Wang, and Richard K. DeFreez. "Periodic and Chaotic Beam Scanning in Semiconductor Laser Arrays." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.pdp4.

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Winful, Herbert G., Shawe-Shiuan Wang, and Richard K. DcFreez. "Spontaneous Periodic and Chaotic Beam Scanning in Semiconductor Laser Arrays." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.sdslad119.

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De Jagher, P. C., and D. Lenstra. "The modulated semiconductor laser: a Hamiltonian search for its periodic attractors." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.tha5.

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Modulated lasers have been investigated for over a decade now, c.f. ref. [3] and references cited therein. Periodic as well as chaotic types of operation have been observed. In this paper we put forward a mathematical technique to calculate lower and upper bounds for the modulation strength which is needed to sustain a periodic large amplitude output.
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Pettiaux, Nicolas, and Thomas Erneux. "From harmonic to pulsating periodic solutions in intracavity second harmonic generation." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.mc25.

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We consider the problem of Second Harmonic Generation (SHG) inside a resonant cavity, pumped by an external laser. The elementary process that takes place in SHG is the absorption of 2 photons of frequency ω and the emission of one photon at frequency 2ω. Drummond et al[1] have shown that this problem can be modeled by two ordinary differential equations for the (complex) amplitudes of the electrical fields: where overbar means complex conjugate.
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Royston, Thomas J., and Rajendra Singh. "Periodic Response of Nonlinear Engine Mounting Systems." In SAE Noise and Vibration Conference and Exposition. SAE International, 1995. http://dx.doi.org/10.4271/951297.

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Reports on the topic "Nonlinear periodic systems"

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Mirus, Kevin A. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch. Office of Scientific and Technical Information (OSTI), 1998. http://dx.doi.org/10.2172/656820.

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Soloviev, Vladimir, and Andrey Belinskij. Methods of nonlinear dynamics and the construction of cryptocurrency crisis phenomena precursors. [б. в.], 2018. http://dx.doi.org/10.31812/123456789/2851.

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This article demonstrates the possibility of constructing indicators of critical and crisis phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex systems such as recurrent analysis of dynamic systems and the calculation of permutation entropy are used. It is shown that it is possible to construct dynamic measures of complexity, both recurrent and entropy, which behave in a proper way during actual pre-crisis periods. This fact is used to build predictors of crisis phenomena on the example of the main five crises recorded in the time series o
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Moon, Francis C. Nonlinear dynamics of fluid-structure systems. Final technical report for period January 5, 1991 - December 31, 1997. Office of Scientific and Technical Information (OSTI), 1999. http://dx.doi.org/10.2172/756804.

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Bielinskyi, Andrii O., Oleksandr A. Serdyuk, Сергій Олексійович Семеріков, Володимир Миколайович Соловйов, Андрій Іванович Білінський, and О. А. Сердюк. Econophysics of cryptocurrency crashes: a systematic review. Криворізький державний педагогічний університет, 2021. http://dx.doi.org/10.31812/123456789/6974.

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Cryptocurrencies refer to a type of digital asset that uses distributed ledger, or blockchain technology to enable a secure transaction. Like other financial assets, they show signs of complex systems built from a large number of nonlinearly interacting constituents, which exhibits collective behavior and, due to an exchange of energy or information with the environment, can easily modify its internal structure and patterns of activity. We review the econophysics analysis methods and models adopted in or invented for financial time series and their subtle properties, which are applicable to ti
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Wu, Yingjie, Selim Gunay, and Khalid Mosalam. Hybrid Simulations for the Seismic Evaluation of Resilient Highway Bridge Systems. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, 2020. http://dx.doi.org/10.55461/ytgv8834.

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Bridges often serve as key links in local and national transportation networks. Bridge closures can result in severe costs, not only in the form of repair or replacement, but also in the form of economic losses related to medium- and long-term interruption of businesses and disruption to surrounding communities. In addition, continuous functionality of bridges is very important after any seismic event for emergency response and recovery purposes. Considering the importance of these structures, the associated structural design philosophy is shifting from collapse prevention to maintaining funct
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