Journal articles: 'Nonlinear dynamics'

1

Smirnov, V. V., M. A. Kovaleva, and L. I. Manevitch. "Nonlinear Dynamics of Torsion Lattices." Nelineinaya Dinamika 14, no. 2 (2018): 179–93. http://dx.doi.org/10.20537/nd180203.

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Lopes, António, and J. Machado. "Nonlinear Dynamics." Mathematics 10, no. 15 (July 30, 2022): 2702. http://dx.doi.org/10.3390/math10152702.

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Smirnov, V. V., and L. I. Manevitch. "Complex Envelope Variable Approximation in Nonlinear Dynamics." Nelineinaya Dinamika 16, no. 3 (2020): 491–515. http://dx.doi.org/10.20537/nd200307.

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Mureithi, Njuki W. "Karman Wake Dynamics and Vortex Induced Vibration Control : A Nonlinear Dynamics Perspective." Proceedings of the Dynamics & Design Conference 2008 (2008): _B1–1_—_B1–6_. http://dx.doi.org/10.1299/jsmedmc.2008._b1-1_.

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Редакционная, Статья. "Seminar “Nonlinear Dynamics”." Modeling and Analysis of Information Systems 21, no. 6 (January 1, 2014): 176–92. http://dx.doi.org/10.18255/1818-1015-2014-6-176-192.

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6

DeCoster, Gregory P., and Douglas W. Mitchell. "Nonlinear Monetary Dynamics." Journal of Business & Economic Statistics 9, no. 4 (October 1991): 455. http://dx.doi.org/10.2307/1391245.

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Benhabib, Jess, and Jean-Michel Grandmont. "Nonlinear Economic Dynamics." Economica 55, no. 219 (August 1988): 420. http://dx.doi.org/10.2307/2554021.

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DeCoster, Gregory P., and Douglas W. Mitchell. "Nonlinear Monetary Dynamics." Journal of Business & Economic Statistics 9, no. 4 (October 1991): 455–61. http://dx.doi.org/10.1080/07350015.1991.10509872.

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9

Kaplan, Daniel, Leon Glass, and Stanley A. Berger. "Understanding Nonlinear Dynamics." Physics Today 49, no. 2 (February 1996): 62. http://dx.doi.org/10.1063/1.2807512.

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10

Sagués, Francesc, and Irving R. Epstein. "Nonlinear chemical dynamics." Dalton Transactions, no. 7 (March 10, 2003): 1201–17. http://dx.doi.org/10.1039/b210932h.

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Prosperetti, Andrea, Lawrence A. Crum, and Kerry W. Commander. "Nonlinear bubble dynamics." Journal of the Acoustical Society of America 83, no. 2 (February 1988): 502–14. http://dx.doi.org/10.1121/1.396145.

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Gluckman, Bruce J. "Experimental nonlinear dynamics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1918 (May 13, 2010): 2143–46. http://dx.doi.org/10.1098/rsta.2010.0062.

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Bramante, Riccardo, Gimmi Dallago, and Silvia Facchinetti. "Nonlinear relative dynamics." European Journal of Finance 26, no. 13 (March 23, 2020): 1301–14. http://dx.doi.org/10.1080/1351847x.2020.1742757.

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Krebs, Charles J. "Nonlinear population dynamics." Trends in Ecology & Evolution 18, no. 12 (December 2003): 615. http://dx.doi.org/10.1016/j.tree.2003.08.004.

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Feng, Z. C., and L. G. Leal. "NONLINEAR BUBBLE DYNAMICS." Annual Review of Fluid Mechanics 29, no. 1 (January 1997): 201–43. http://dx.doi.org/10.1146/annurev.fluid.29.1.201.

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Kozochkin, M. P. "Nonlinear cutting dynamics." Russian Engineering Research 32, no. 4 (April 2012): 387–91. http://dx.doi.org/10.3103/s1068798x12040168.

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Kawamura, Naoya, Wataru Sato, Koh Shimokawa, Tomohiro Fujita, and Yasutomo Kawanishi. "Machine Learning-Based Interpretable Modeling for Subjective Emotional Dynamics Sensing Using Facial EMG." Sensors 24, no. 5 (February 27, 2024): 1536. http://dx.doi.org/10.3390/s24051536.

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Understanding the association between subjective emotional experiences and physiological signals is of practical and theoretical significance. Previous psychophysiological studies have shown a linear relationship between dynamic emotional valence experiences and facial electromyography (EMG) activities. However, whether and how subjective emotional valence dynamics relate to facial EMG changes nonlinearly remains unknown. To investigate this issue, we re-analyzed the data of two previous studies that measured dynamic valence ratings and facial EMG of the corrugator supercilii and zygomatic major muscles from 50 participants who viewed emotional film clips. We employed multilinear regression analyses and two nonlinear machine learning (ML) models: random forest and long short-term memory. In cross-validation, these ML models outperformed linear regression in terms of the mean squared error and correlation coefficient. Interpretation of the random forest model using the SHapley Additive exPlanation tool revealed nonlinear and interactive associations between several EMG features and subjective valence dynamics. These findings suggest that nonlinear ML models can better fit the relationship between subjective emotional valence dynamics and facial EMG than conventional linear models and highlight a nonlinear and complex relationship. The findings encourage emotion sensing using facial EMG and offer insight into the subjective–physiological association.

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18

Snippe, H. P., and J. H. van Hateren. "Dynamics of Nonlinear Feedback Control." Neural Computation 19, no. 5 (May 2007): 1179–214. http://dx.doi.org/10.1162/neco.2007.19.5.1179.

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Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input steps, the dynamics of gain and attenuation can be very different, depending on the mathematical form of the nonlinearity and the ordering of the nonlinearity and the filtering in the feedback loop. Further, the dynamics of feedback control can be strongly asymmetrical for increment versus decrement steps of the input. Nevertheless, for each of the models studied, the nonlinearity in the feedback loop can be chosen such that immediately after an input step, the dynamics of feedback control is symmetric with respect to increments versus decrements. Finally, we study the dynamics of the output of the control loops and find conditions under which overshoots and undershoots of the output relative to the steady-state output occur when the models are stimulated with low-pass filtered steps. For small steps at the input, overshoots and undershoots of the output do not occur when the filtering in the control path is faster than the low-pass filtering at the input. For large steps at the input, however, results depend on the model, and for some of the models, multiple overshoots and undershoots can occur even with a fast control path.

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Ivanchenko, Hennadii, and Serhii Vashchaiev. "Studying the dynamics of nonlinear interaction between enterprise populations." Neuro-Fuzzy Modeling Techniques in Economics 7, no. 1 (May 27, 2019): 44–61. http://dx.doi.org/10.21511/nfmte.7.2018.03.

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The article highlights the results of a study of the dynamic evolutionary processes of trophic relations between populations of enterprises. A model based on differential equations is constructed, which describes the economic system and takes into account the dynamics of the specific income of competing populations of enterprises in relations of protocooperation, nonlinearity of growth and competition. This model can be used to analyze the dynamics of transient processes in various life cycle scenarios and predict the synergistic effect of mergers and acquisitions. A bifurcation analysis of possible scenarios of dynamic modes of merger and acquisition processes using the neural network system of pattern recognition was carried out. To this end, a Kohonen self-organizing map has been constructed, which recognizes phase portraits of bifurcation diagrams of enterprises life cycle into five separate classes in accordance with the scenarios of their development. As a result of the experimental study, characteristic modes of the evolution of economic systems were revealed, and also conclusions were made on the mechanisms of influence of the external environment and internal structure on the regime of evolution of populations of enterprises.

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20

Piprek, Patrick, Michael M. Marb, Pranav Bhardwaj, and Florian Holzapfel. "Trajectory/Path-Following Controller Based on Nonlinear Jerk-Level Error Dynamics." Applied Sciences 10, no. 23 (December 7, 2020): 8760. http://dx.doi.org/10.3390/app10238760.

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This study proposes a novel, nonlinear trajectory/path-following controller based on jerk-level error dynamics. Therefore, at first the nonlinear acceleration-based kinematic equations of motion of a dynamic system are differentiated with respect to time to obtain a representation connecting the translation jerk with the (specific) force derivative. Furthermore, the path deviation, i.e., the difference between the planned and the actual path, is formulated as nonlinear error dynamics based on the jerk error. Combining the derived equations of motion with the nonlinear error dynamics as well as employing nonlinear dynamic inversion, a control law can be derived that provides force derivative commands, which may be commanded to an inner loop for trajectory control. This command ensures an increased smoothness and faster reaction time compared to traditional approaches based on a force directly. Furthermore, the nonlinear parts in the error dynamic are feedforward components that improve the general performance due to their physical connection with the real dynamics. The validity and performance of the proposed trajectory/path-following controller are shown in an aircraft-related application example.

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21

Gouskov, A. M., M. A. Guskov, D. D. Tung, and G. Y. Panovko. "Nonlinear Regenerative Dynamics Analysis of the Multicutter Turning Process." Nelineinaya Dinamika 15, no. 2 (2019): 145–58. http://dx.doi.org/10.20537/nd190204.

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22

Munch, Stephan B., Antoine Brias, George Sugihara, and Tanya L. Rogers. "Frequently asked questions about nonlinear dynamics and empirical dynamic modelling." ICES Journal of Marine Science 77, no. 4 (November 26, 2019): 1463–79. http://dx.doi.org/10.1093/icesjms/fsz209.

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Abstract Complex nonlinear dynamics are ubiquitous in marine ecology. Empirical dynamic modelling can be used to infer ecosystem dynamics and species interactions while making minimal assumptions. Although there is growing enthusiasm for applying these methods, the background required to understand them is not typically part of contemporary marine ecology curricula, leading to numerous questions and potential misunderstanding. In this study, we provide a brief overview of empirical dynamic modelling, followed by answers to the ten most frequently asked questions about nonlinear dynamics and nonlinear forecasting.

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23

Gebrel, Ibrahim F., and Samuel F. Asokanthan. "Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes." Vibration 4, no. 4 (October 25, 2021): 805–21. http://dx.doi.org/10.3390/vibration4040045.

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This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure. Understanding the effects of nonlinear actuator dynamics is essential for characterizing the dynamic behavior of such devices. For this purpose, a suitable theoretical model to generate a nonlinear electrostatic force acting on the MEMS ring structure is formulated. Nonlinear dynamic responses in the driving and sensing directions are examined via time response, phase diagram, and Poincare’s map when the input angular motion and nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid ongoing research associated with the fabrication of this type of device and provide design improvements in MEMS ring-based gyroscopes.

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24

Tyukin, Ivan, and Cees van Leeuwen. "ADAPTATION AND NONLINEAR PARAMETRIZATION: NONLINEAR DYNAMICS PROSPECTIVE." IFAC Proceedings Volumes 38, no. 1 (2005): 223–28. http://dx.doi.org/10.3182/20050703-6-cz-1902.00258.

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25

Schilhabel, T. E., and C. J. Harris. "Nonlinear Estimation of Population Coded Nonlinear Dynamics." IFAC Proceedings Volumes 31, no. 29 (October 1998): 70. http://dx.doi.org/10.1016/s1474-6670(17)38357-x.

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26

Goriely, Alain, and Michael Tabor. "Nonlinear dynamics of filaments II. Nonlinear analysis." Physica D: Nonlinear Phenomena 105, no. 1-3 (June 1997): 45–61. http://dx.doi.org/10.1016/s0167-2789(97)83389-1.

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27

PAVEL, Marilena D. "Particularities of Rotorcraft in Dealing with Advanced Controllers." INCAS BULLETIN 16, no. 2 (June 10, 2024): 85–97. http://dx.doi.org/10.13111/2066-8201.2024.16.2.7.

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Advanced nonlinear controllers are a desirable solution to rotorcraft flight control as they can solve the system high nonlinear dynamic behavior. However, conventional nonlinear controllers such as Nonlinear Dynamic Inversion (NDI) controller heavily rely on the availability of accurate model knowledge and this can be problematic for rotorcraft. Therefore, incremental control theory can solve the modelling errors sensitivity by relying on the information obtained from the sensors instead. The paper applied the Incremental Nonlinear Dynamic Inversion (INDI) controller to rotorcraft case. It will be demonstrated that, for rotorcraft, the incremental nonlinear controllers depend on the delays introduced in the controller by the rotor dynamics. To correct this behaviour, residualization and synchronization methods need to be applied accordingly in order to remove the effects of rotor flapping (disctilt) dynamics from the controller. These particularities of rotorcraft in dealing with advanced controllers shows that incremental nonlinear controllers can have relatively small stability robustness margin and careful controller design is needed in order to account properly for rotorcraft time delays and unmodelled dynamics.

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28

Wu, Zhe, Guang Yang, Qiang Zhang, Shengyue Tan, and Shuyong Hou. "Information Dynamic Correlation of Vibration in Nonlinear Systems." Entropy 22, no. 1 (December 31, 2019): 56. http://dx.doi.org/10.3390/e22010056.

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In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics.

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29

Yuan, Ying Cai, Yan Li, and Yi Ming Wang. "Robust Design to Control the Chaos of Fold Mechanism with Clearance." Applied Mechanics and Materials 312 (February 2013): 153–57. http://dx.doi.org/10.4028/www.scientific.net/amm.312.153.

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With the increasing of web offset printing machines working speed, the nonlinear dynamics responses are more significant, even the fold mechanism with clearances appears some chaos phenomenon. Based on the dynamic model of fold mechanism, the nonlinear dynamics responses and the chaos movement in pair are studied. Used the performance parameters and dynamics response sensitivities as the goal values, the robust design model is established. By the robust design model, the nonlinear dynamic responses and chaos phenomenon can be under controlled in the same clearance degree. In this way, the performance of fold mechanism may be improved.

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30

Ravochkin, N. N. "Procedural world nonlinear dynamics." Ekonomicheskie i sotsial’no-gumanitarnye issledovaniya, no. 1(29) (2021): 62–71. http://dx.doi.org/10.24151/2409-1073-2021-1-62-71.

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In this article, the author attempts to uncover and then critically analyze the nonlinear world dynamics of the leading trend of our time. Close attention is paid to the place and role of social processes that contribute to the growth of nonlinearity and unpredictability of modern world dynamics. The meaning of the synergetic concept is clarified when considering the dynamics of the present world. Shows the variability of modern social relations. The essence of the self-determinability of the world is presented. The hierarchization of modern social systems is determined.

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31

Guckenheimer, John M., and E. Atlee Jackson. "Perspectives of Nonlinear Dynamics." American Mathematical Monthly 97, no. 6 (June 1990): 544. http://dx.doi.org/10.2307/2323851.

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32

Whitley, D. C., J. M. T. Thompson, and H. B. Stewart. "Nonlinear Dynamics and Chaos." Mathematical Gazette 71, no. 456 (June 1987): 169. http://dx.doi.org/10.2307/3616531.

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33

Letellier, C., L. Le Sceller, and G. Gouesbet. "NONLINEAR DYNAMICS : WHAT FOR ?" High Temperature Material Processes (An International Quarterly of High-Technology Plasma Processes) 2, no. 1 (1998): 83–101. http://dx.doi.org/10.1615/hightempmatproc.v2.i1.70.

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34

Arrowsmith, D. "NONLINEAR DYNAMICS AND CHAOS." Bulletin of the London Mathematical Society 19, no. 4 (July 1987): 404–5. http://dx.doi.org/10.1112/blms/19.4.404.

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35

Thompson, J. M. T., H. B. Stewart, and Rick Turner. "Nonlinear Dynamics and Chaos." Computers in Physics 4, no. 5 (1990): 562. http://dx.doi.org/10.1063/1.4822949.

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36

Medak, B., and A. A. Tret’yakov. "p-Regular nonlinear dynamics." Doklady Mathematics 89, no. 1 (January 2014): 112–14. http://dx.doi.org/10.1134/s1064562414010335.

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37

Krogh-Madsen, Trine, and David J. Christini. "Nonlinear Dynamics in Cardiology." Annual Review of Biomedical Engineering 14, no. 1 (August 15, 2012): 179–203. http://dx.doi.org/10.1146/annurev-bioeng-071811-150106.

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38

Lim, Chjan C., and Lawrence Sirovich. "Nonlinear vortex trail dynamics." Physics of Fluids 31, no. 5 (1988): 991. http://dx.doi.org/10.1063/1.866719.

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39

Han, Maoan, Zhen Jin, Yonghui Xia, and Haomin Zhou. "Dynamics of Nonlinear Systems." Scientific World Journal 2014 (2014): 1. http://dx.doi.org/10.1155/2014/246418.

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40

KAR, SANDIP, and DEB SHANKAR RAY. "NONLINEAR DYNAMICS OF GLYCOLYSIS." Modern Physics Letters B 18, no. 14 (June 10, 2004): 653–78. http://dx.doi.org/10.1142/s0217984904007207.

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Glycolysis is the most important cellular process yielding ATP, the universal energy carrier molecule in all living organisms. The characteristic oscillations of the intermediates of glycolysis have been the subject of extensive experimental and theoretical research over the last four decades. A conspicuous property of the glycolytic oscillations is their critical control by the substrate injection rate. In this brief review, we trace its experimental background and explore the essential underlying theoretical models to elucidate a number of nonlinear dynamical phenomena observed in the weak noise limit of the substrate injection rate. Simultaneous oscillations of glycolytic intermediates and insulin have also been discussed within the framework of a phenomenological model in the context of basic experimental issues.

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41

Tret'yakov, Alexey A., and Beata Medak. "P-regular nonlinear dynamics." Topological Methods in Nonlinear Analysis 46, no. 1 (September 1, 2015): 283. http://dx.doi.org/10.12775/tmna.2015.047.

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42

Tadayon, M. A., M. Rajaei, H. Sayyaadi, G. Nakhaie Jazar, and A. Alasty. "Nonlinear Dynamics of MicroResonators." Journal of Physics: Conference Series 34 (April 1, 2006): 961–66. http://dx.doi.org/10.1088/1742-6596/34/1/159.

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43

Germay, Christophe, Nathan Van de Wouw, Henk Nijmeijer, and Rodolphe Sepulchre. "Nonlinear Drillstring Dynamics Analysis." SIAM Journal on Applied Dynamical Systems 8, no. 2 (January 2009): 527–53. http://dx.doi.org/10.1137/060675848.

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44

Van Orden, Guy. "Nonlinear Dynamics and Psycholinguistics." Ecological Psychology 14, no. 1 (April 1, 2002): 1–4. http://dx.doi.org/10.1207/s15326969eco1401&2double_1.

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45

Pajevic, Sinisa. "Nonlinear dynamics and chaos." Journal of Statistical Physics 78, no. 5-6 (March 1995): 1635–36. http://dx.doi.org/10.1007/bf02180148.

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46

Constantin, Peter. "Nonlinear inviscid incompressible dynamics." Physica D: Nonlinear Phenomena 86, no. 1-2 (September 1995): 212–19. http://dx.doi.org/10.1016/0167-2789(95)00102-a.

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Van Orden, Guy C. "Nonlinear Dynamics and Psycholinguistics." Ecological Psychology 14, no. 1-2 (April 2002): 1–4. http://dx.doi.org/10.1080/10407413.2003.9652749.

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48

Ghayesh, Mergen H., and Hamed Farokhi. "Nonlinear dynamics of microplates." International Journal of Engineering Science 86 (January 2015): 60–73. http://dx.doi.org/10.1016/j.ijengsci.2014.10.004.

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ERMENTROUT, G. "Perspectives of nonlinear dynamics." Bulletin of Mathematical Biology 53, no. 6 (1991): 946–48. http://dx.doi.org/10.1016/s0092-8240(05)80416-1.

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Macmillen, F. B. J. "Nonlinear flight dynamics analysis." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 356, no. 1745 (October 15, 1998): 2167–80. http://dx.doi.org/10.1098/rsta.1998.0268.

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Journal articles on the topic 'Nonlinear dynamics'

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