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Journal articles on the topic 'Chaos experiment'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Brun, E. "Deterministisches Chaos im Experiment." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 69, no. 7 (1989): 171–74. http://dx.doi.org/10.1002/zamm.19890690702.

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2

Davies, Brian, and Robert C. Hilborn. "Exploring Chaos: Theory and Experiment." American Journal of Physics 68, no. 5 (May 2000): 489–90. http://dx.doi.org/10.1119/1.19464.

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3

Borcherds, P. "Exploring Chaos: Theory and Experiment." European Journal of Physics 21, no. 1 (January 1, 2000): 118. http://dx.doi.org/10.1088/0143-0807/21/1/503.

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4

Levien, R. B., and S. M. Tan. "Double pendulum: An experiment in chaos." American Journal of Physics 61, no. 11 (November 1993): 1038–44. http://dx.doi.org/10.1119/1.17335.

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5

Muñoz, L., R. A. Molina, and J. M. G. Gómez. "Chaos in nuclei: Theory and experiment." Journal of Physics: Conference Series 1023 (May 2018): 012011. http://dx.doi.org/10.1088/1742-6596/1023/1/012011.

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6

Dionne, Gregory E., and Richard L. Liboff. "Waveguide experiment related to field chaos." Physics Letters A 204, no. 2 (August 1995): 174–76. http://dx.doi.org/10.1016/0375-9601(95)00422-y.

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7

Chen, Yu Qiang, and Na Xin Peng. "Study on Chaotic Particle Swarm Optimization Algorithm in Solution of Logistics Scheduling Problem." Advanced Materials Research 798-799 (September 2013): 720–27. http://dx.doi.org/10.4028/www.scientific.net/amr.798-799.720.

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Study the basic theory and process of chaos particle swarm optimization (PSO) algorithm, improve the basic PSO algorithm by introducing the self-adaptive inertia weighting factor method. Construct the mathematical model of basic logistics scheduling to complete the simulation analysis experiments. Experiment results show that self-adaptive chaos particle swarm optimization algorithm is effective and feasible to solve the logistics scheduling model problem.

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8

Ananthakrishna, G., and S. J. Noronha. "Chaos in Jerky Flow: Theory and Experiment." Solid State Phenomena 42-43 (April 1995): 277–86. http://dx.doi.org/10.4028/www.scientific.net/ssp.42-43.277.

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9

Matsumoto, T., L. Chua, and K. Kobayashi. "Hyper chaos: Laboratory experiment and numerical confirmation." IEEE Transactions on Circuits and Systems 33, no. 11 (November 1986): 1143–47. http://dx.doi.org/10.1109/tcs.1986.1085862.

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10

BRAUER, ECKART, STEFAN BLOCHWITZ, and HORST BEIGE. "PERIODIC WINDOWS INSIDE CHAOS — EXPERIMENT VERSUS THEORY." International Journal of Bifurcation and Chaos 04, no. 04 (August 1994): 1031–39. http://dx.doi.org/10.1142/s0218127494000745.

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A series resonance circuit that consists of a linear inductance, a nonlinear capacitance and a sinusoidal driving is investigated. The nonlinearity arises from a ferroelectric crystal. We observed the Feigenbaum scenario, crises, periodic windows inside chaos that show a period adding behaviour and coexisting attractors of different symmetry. We conclude a Duffing equation to cover all significant properties of our dynamical system.

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11

Natarajan, Priyamvada. "Cosmos, Chaos and Order: Mapping as Knowing." Leonardo 54, no. 1 (February 2021): 107–14. http://dx.doi.org/10.1162/leon_a_01989.

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Observation and experiment are seen as the cornerstones of empirical science. Astronomy, an inherently observational science, affords a case study of a discipline in which controlled experiments cannot be performed. The author argues that in such disciplines maps and mapping serve to interpolate intellectually between observation and experiment. This is particularly noticeable in the early conceptions of cosmos and changes in worldview wherein major cognitive shifts are encoded in maps. With historical advances in map-making techniques, the epistemic purposes served by maps have also evolved significantly. Maps in astronomy today are deployed as powerful visual devices that record and transmute observational data to support theoretical ideas underpinning our current understanding of the cosmos. One example is dark matter maps, which offer compelling indirect evidence for the existence of the elusive dominant matter component that shapes our universe: dark matter.

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12

Chen, Hong, Cheng Chen, and Shu Bin Gu. "UPT Chaos-Based Encryption Characteristic Analysis for Speech Signal." Applied Mechanics and Materials 713-715 (January 2015): 1456–59. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1456.

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In chaotic speech signal encryption, masking is the most direct and convenient method. But the chaotic signals usually have a narrow spectral range in low frequency region. In order to overcome the disadvantage that the higher frequency signals can not be completely covered up, UPT is used to conduct a nonlinear transformation to chaotic signal. After UPT, chaotic types are increased, chaotic characteristics are improved and spectral range is widened. Simulation experiments are done respectively from frequency domain and spectrogram perspectives. The chaos before and after transformation are used to mask speech signal. Decoding experiment is taken on the speech encrypted by transformed chaos. Experiment results show that, after UPT, the encryption effect of speech signal is improved obviously. This method has a high security and a strong anti-attack ability.

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13

Argentina, Médéric, Pierre Coullet, Jean-Marc Gilli, Marc Monticelli, and Germain Rousseaux. "Chaos in Robert Hooke's inverted cone." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2081 (February 13, 2007): 1259–69. http://dx.doi.org/10.1098/rspa.2007.1813.

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Robert Hooke is perhaps one of the first scientists to have met chaotic motions. Indeed, to invert a cone and let a ball move in it was a mechanical model used by him to mimic the motion of a planet around a centre of force like the Sun. However, as the cone is inclined with respect to the gravity field, the perfect rosace followed by the particle becomes chaotic meanderings. We revisit this classical experiment designed by Hooke with the modern tools of dynamical systems and chaos theory. By a combination of both numerical simulations and experiments, we prove that the scenario of transition to the chaotic behaviour is through a period-doubling instability.

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14

Li, Jin Hai. "Experiment Study of Chaos Motion of Cable-Stayed." Applied Mechanics and Materials 444-445 (October 2013): 748–52. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.748.

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The cable-stayed is one of the principal force members of cable-stayed bridges. It would be prone to exhibit vibration of large amplitude on the action of wind, earthquake and traffic load,so it reduces the life of stayed cable and even cause destruction. In order to reduce the cable damage, it is very necessary to study the mechanism of vibration of cable-stayed. Experiments are conducted to explore the nonlinear vibration of cable under the periodic external force. A cable model with 14.3 meters long is set up and an acceleration sensor is installed on the midpoint of cable. Time-history acceleration data are obtained by using of acceleration sensor under three cycle load. From the data a Poincare Map is provided and chaos motion is confirmed by using of Smale Horseshoe Map theory.

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15

Jánosi, Imre M., Leci Flepp, and Tamás Tél. "Exploring transient chaos in an NMR-laser experiment." Physical Review Letters 73, no. 4 (July 25, 1994): 529–32. http://dx.doi.org/10.1103/physrevlett.73.529.

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16

Ding, Mingzhou, Weiming Yang, Visarath In, William L. Ditto, Mark L. Spano, and Bruce Gluckman. "Controlling chaos in high dimensions: Theory and experiment." Physical Review E 53, no. 5 (May 1, 1996): 4334–44. http://dx.doi.org/10.1103/physreve.53.4334.

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17

Belotserkovskii, O. M. "Numerical Experiment in Turbulence: from Order to Chaos." International Journal of Fluid Mechanics Research 23, no. 5-6 (1996): 321–488. http://dx.doi.org/10.1615/interjfluidmechres.v23.i5-6.10.

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18

Spano, M. L., W. L. Ditto, and S. N. Rauseo. "Exploitation of Chaos for Active Control: An Experiment." Journal of Intelligent Material Systems and Structures 2, no. 4 (October 1991): 482–93. http://dx.doi.org/10.1177/1045389x9100200404.

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19

Neuringer, Allen, and Cheryl Voss. "Approximating Chaotic Behavior." Psychological Science 4, no. 2 (March 1993): 113–19. http://dx.doi.org/10.1111/j.1467-9280.1993.tb00471.x.

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Human subjects received feedback showing how closely their responses approximated the chaotic output of the logistic difference function. In Experiment 1, subjects generated analog responses by placing a pointer along a line. In Experiment 2, they generated digital responses in the form of three-digit numbers. In Experiment 3, feedback was sometimes provided and other times withheld. Responses came to approximate three defining characteristics of logistic chaos: Sequences were “noisy,” they were extremely sensitive to initial conditions, and lag 1 autocorrelation functions were parabolic in form. Chaos theory may describe some highly variable although precisely determined human behaviors.

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20

Cavalcante, Hugo L. D. de S., Daniel J. Gauthier, Joshua E. S. Socolar, and Rui Zhang. "On the origin of chaos in autonomous Boolean networks." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1911 (January 28, 2010): 495–513. http://dx.doi.org/10.1098/rsta.2009.0235.

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We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic behaviour or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power law. In an experiment, the non-ideal behaviour of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and asymmetry between the logic states tend to engender periodic behaviour, at least for the simplest networks. On the other hand, we find that a memory effect termed ‘degradation’ can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices may find application in a variety of technologies requiring fast complex waveforms or flat power spectra, and can be used as a test-bed for fundamental studies of real-world Boolean-like networks.

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21

Gunaratne, Gemunu H., Paul S. Linsay, and Michael J. Vinson. "Chaos beyond onset: A comparison of theory and experiment." Physical Review Letters 63, no. 1 (July 3, 1989): 1–4. http://dx.doi.org/10.1103/physrevlett.63.1.

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22

Khurana, Anil. "Rayleigh‐Bénard Experiment Probes Transition from Chaos to Turbulence." Physics Today 41, no. 6 (June 1988): 17–21. http://dx.doi.org/10.1063/1.2811443.

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23

Watts, Christopher, D. E. Newman, and J. C. Sprott. "Chaos in reversed-field-pinch plasma simulation and experiment." Physical Review E 49, no. 3 (March 1, 1994): 2291–301. http://dx.doi.org/10.1103/physreve.49.2291.

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24

Fajraoui, Noura, Stefano Marelli, and Bruno Sudret. "Sequential Design of Experiment for Sparse Polynomial Chaos Expansions." SIAM/ASA Journal on Uncertainty Quantification 5, no. 1 (January 2017): 1061–85. http://dx.doi.org/10.1137/16m1103488.

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25

Lonngren, K. E. "Notes to accompany a student laboratory experiment on chaos." IEEE Transactions on Education 34, no. 1 (1991): 123–28. http://dx.doi.org/10.1109/13.79892.

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26

Stoop, R., J. Peinke, J. Parisi, B. Röhricht, and R. P. Huebener. "A p-Ge semiconductor experiment showing chaos and hyperchaos." Physica D: Nonlinear Phenomena 35, no. 3 (May 1989): 425–35. http://dx.doi.org/10.1016/0167-2789(89)90078-x.

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27

Zhen, Wang, and Xue Feng Liu. "The Simulation and Research of Chaos in Current-Controlled Boost DC / DC Converter." Advanced Materials Research 383-390 (November 2011): 553–57. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.553.

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For the non-linear phenomena of the switching power supply, the discrete mathematical model of current-controlled Boost DC/DC converter has been presented in this paper, according to the switch maps. The results of simulation and experiment are derived, and the variable is the current of inductor. The accuracy of the model has been verified by the results of simulation and experiment which reveales the DC / DC converters from the bifurcation and eventually to the phenomenon of chaos. The theoretical basis using or avoiding chaos is provided for the power supply design.

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28

Yang, Dong, Zhiqin Kang, and Yangsheng Zhao. "Mechanism of the Gas-Liquid Two-Phase Chaotic Flow in Single Fracture." Geofluids 2020 (August 25, 2020): 1–11. http://dx.doi.org/10.1155/2020/8860058.

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The seepage of gas-liquid two-phase flow in fracture is a commonly found phenomenon in nature. To reveal the underlying mechanism and the critical condition of the chaos occurrence, a stochastic gas-liquid two-phase flow seepage model is established, and then investigated through a numerical simulation and a horizontal Hele-Shaw experiment. The numerical simulation and laboratory experiment results show that the seepage chaos of gas-liquid two-phase flow takes place when the relative saturation is in the range of gas relative saturation 44%-70%, and the occurrence probability can be expressed in polynomials. The chaos probability exceeds 80% when the relative saturation of gas is 47%-65%, and the chaos probability is 100% when the relative gas saturation is 57%-60%. It is found that the stochastic variation of gas connection cluster and the compressibility of gas lead to a remarkable change of pressure gradient of the gas-liquid flow both in magnitude and direction. Therefore, the turbulent flow is formed, the kinetic energy of fluid transport decreases gradually, and the flow is stopped at last.

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29

Mendoza, Benjamín David, Diego Alberto Lara, Jehú López-Aparicio, Gustavo Armendáriz, Leonardo López-Hernández, Víctor Velázquez, Edna Magdalena Hernández, Marcela Grether, Enrique López-Moreno, and Alejandro Frank. "Quantum Chaos in Time Series of Single Photons as a Superposition of Wave and Particle States." Photonics 8, no. 8 (August 11, 2021): 326. http://dx.doi.org/10.3390/photonics8080326.

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We build a time series of single photons with quantum chaos statistics, using a version of the Grangier anti-correlation experiment. The criteria utilized to determine the presence of quantum chaos is the frame of the Fano factor and the power spectrum. We also show that photons with chaotic statistics are in a balanced superposition of photons with both wave-like and particle like behaviors. To support the presence of quantum chaos, we study both Shannon’s entropy, and the complexity of single photons time series.

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30

Tang, Wallace K. S., and Marius-F. Danca. "Emulating “Chaos + Chaos = Order” in Chen’s Circuit of Fractional Order by Parameter Switching." International Journal of Bifurcation and Chaos 26, no. 06 (June 15, 2016): 1650096. http://dx.doi.org/10.1142/s0218127416500966.

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In this paper, the effect of the parameter switching (PS) algorithm in a fractional order chaotic circuit is investigated both in simulation and experiment. The Chen system of fractional order is focused and realized in an electronic circuit. By designing a switching circuit, the PS algorithm is implemented and it is the first time, the paradoxical “Chaos [Formula: see text] Chaos [Formula: see text] Order” is presented in an electronic circuit. Both the simulation and experimental results confirm that the obtained attractor under switching approximates the attractor of the time-averaged model. Some important design issues for the circuitry realization of the PS scheme are pointed out. Finally, our work confirms the practical usage of PS algorithm in potential applications such as attractor synthesis and chaos control.

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31

Wu, Lin, Jin Cheng Wei, and Liu Jie. "Chaos Synchronization of Hyperchaos Rossler System." Applied Mechanics and Materials 687-691 (November 2014): 724–27. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.724.

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Taking the hyperchaos Rossler system as an example and based on the Lyapunov Stabilization Law, with the parameters unknown, through the designing of controller, the synchronization of the driving system and the responding system has been realized by using the nonlinear feedback controlling method. This method provides a convenient way for the synchrocontrol of hyperchaos system, whose effectiveness has been further proved by the numerical simulation experiment.

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32

Tian, Chang Liu, Xue Li Cheng, and Wei Wang. "Experimental Study on Rock Breaking with Impacting Water Jet by Modulation of Chaos." Advanced Materials Research 535-537 (June 2012): 1751–54. http://dx.doi.org/10.4028/www.scientific.net/amr.535-537.1751.

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The experiment focused on the contrast with rock breaking effect of impacting water jet by modulation of chaos and common cavitation jet. Investigated the influences of various water jet parameters and conditions on rock breaking, such as standoff distance, pump pressure, transverse speed and erosion time and the mass loss and erosion depth were measured in the experiment. The results show that the impacting water jet by modulation of chaos can efficiently use the energy of water jet and increase ability in rock-breaking, which will have a wide application prospect in high pressure water jet technology field.

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33

Lin, Xiaoran, Shangbo Zhou, and Hua Li. "Chaos and Synchronization in Complex Fractional-Order Chua’s System." International Journal of Bifurcation and Chaos 26, no. 03 (March 2016): 1650046. http://dx.doi.org/10.1142/s0218127416500462.

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In this paper, chaos in complex-order Chua’s system and its chaotic synchronization for secure communication are studied based on the fractional derivative investigated. Chaos in complex-order Chua’s system is illustrated by presenting its waveform graphs, states diagrams and bifurcation graphs. The dynamic behaviors in the complex-order Chua’s system and time-delayed Chua’s system are compared. In addition, the largest Lyapunov exponents of normal and time-delayed Chua’s systems are calculated and verified by numerical simulations. The experiment indicates that the chaos in such Chua’s system can achieve two channel communications.

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34

Parisi, J., R. Badii, E. Brun, L. Flepp, C. Reyl, R. Stoop, O. E. Rössler, A. Kittel, and R. Richter. "Explicit Realization of Chaos Control in an NMR-Laser Experiment." Zeitschrift für Naturforschung A 48, no. 5-6 (June 1, 1993): 627–28. http://dx.doi.org/10.1515/zna-1993-5-604.

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Abstract The usefulness of the Ott-Grebogi-Yorke control method is demonstrated by stabilizing a chaotic NMR-laser system around an unstable period-one orbit. We have used a six-dimensional delay-coordinate embedding technique in order to fully determine the stability properties of the orbit controlled. Our analysis yields small time-dependent perturbations of the system quality factor capable to perform real-time control.

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35

Gekelman, Walter, Patrick Pribyl, Henry Birge-Lee, Joe Wise, Cami Katz, Ben Wolman, Bob Baker, et al. "Drift waves and chaos in a LAPTAG plasma physics experiment." American Journal of Physics 84, no. 2 (February 2016): 118–26. http://dx.doi.org/10.1119/1.4936460.

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36

Hammad, A. A., and E. A. Jonckheere. "Taming chaos: a numerical experiment using low-order LTI filters." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 42, no. 2 (1995): 111–15. http://dx.doi.org/10.1109/81.372851.

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37

Benincà, Elisa, Jef Huisman, Reinhard Heerkloss, Klaus D. Jöhnk, Pedro Branco, Egbert H. Van Nes, Marten Scheffer, and Stephen P. Ellner. "Chaos in a long-term experiment with a plankton community." Nature 451, no. 7180 (February 2008): 822–25. http://dx.doi.org/10.1038/nature06512.

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38

Shults, F. LeRon. "A Theology of Chaos. An Experiment in Postmodern Theological Science." Scottish Journal of Theology 45, no. 2 (May 1992): 223–36. http://dx.doi.org/10.1017/s0036930600038667.

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Judeo-Christian theology has always been concerned with the order and rationality of the created universe, believing that this rational order was somehow bestowed upon it by the Creator. However, in the last two decades traditional conceptions of order have been challenged by the scientific discovery that ‘chaos’ permeates the behaviour of natural systems in our cosmos. What is the theologian to make of this ‘discovery’? If theology is to speak to the contemporary mind with its postmodern frame of reference, it must carry out its own inquiry vis-à-vis the work of natural science as it explores the intrinsic intelligibility of the created universe.

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39

Guderian, A., A. F. Münster, M. Kraus, and F. W. Schneider. "Electrochemical Chaos Control in a Chemical Reaction: Experiment and Simulation." Journal of Physical Chemistry A 102, no. 26 (June 1998): 5059–64. http://dx.doi.org/10.1021/jp980997g.

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40

Yamada, T., K. Fukushima, and T. Yazaki. "Chaos in an electronic circuit—experiment on coupled oscillator system." Phase Transitions 29, no. 1 (October 1990): 15–20. http://dx.doi.org/10.1080/01411599008207941.

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41

Mork, J., B. Tromborg, and J. Mark. "Chaos in semiconductor lasers with optical feedback: theory and experiment." IEEE Journal of Quantum Electronics 28, no. 1 (1992): 93–108. http://dx.doi.org/10.1109/3.119502.

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42

Sander, Evelyn, and James A. Yorke. "The Many Facets of Chaos." International Journal of Bifurcation and Chaos 25, no. 04 (April 2015): 1530011. http://dx.doi.org/10.1142/s0218127415300116.

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There are many ways that a person can encounter chaos, such as through a time series from a lab experiment, a basin of attraction with fractal boundaries, a map with a crossing of stable and unstable manifolds, a fractal attractor, or in a system for which uncertainty doubles after some time period. These encounters appear so diverse, but the chaos is the same in all of the underlying systems; it is just observed in different ways. We describe these different types of chaos. We then give two conjectures about the types of dynamical behavior that is observable if one randomly picks out a dynamical system without searching for a specific property. In particular, we conjecture that from picking a system at random, one observes (1) only three types of basic invariant sets: periodic orbits, quasiperiodic orbits, and chaotic sets; and (2) that all the definitions of chaos are in agreement.

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43

Liu, Wenbin, Nengsheng Luo, Guo Pan, and Aijia Ouyang. "Chaos Particle Swarm Optimization Algorithm for Optimization Problems." International Journal of Pattern Recognition and Artificial Intelligence 32, no. 11 (July 24, 2018): 1859019. http://dx.doi.org/10.1142/s021800141859019x.

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A chaos particle swarm optimization (CPSO) algorithm based on the chaos operator (CS) is proposed for global optimization problems and parameter inversion of the nonlinear sun shadow model in our study. The CPSO algorithm combines the local search ability of CS and the global search ability of PSO algorithm. The CPSO algorithm can not only solve the global optimization problems effectively, but also address the parameter inversion problems of the date of sun shadow model location successfully. The results of numerical experiment and simulation experiment show that the CPSO algorithm has higher accuracy and faster convergence than the-state-of-the-art techniques. It can effectively improve the computing accuracy and computing efficiency of the global optimization problems, and also provide a novel method to solve the problems of integer parameter inversion in real life.

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44

MARWAN, NORBERT, and ANJA MEINKE. "EXTENDED RECURRENCE PLOT ANALYSIS AND ITS APPLICATION TO ERP DATA." International Journal of Bifurcation and Chaos 14, no. 02 (February 2004): 761–71. http://dx.doi.org/10.1142/s0218127404009454.

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We present new measures of complexity and their application to event-related potential data. The new measures are based on structures of recurrence plots and makes the identification of chaos–chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.

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45

ZHANG, Y., G. H. DU, and J. J. JIANG. "SYNCHRONIZING CHAOS BY IMPULSIVE FEEDBACK METHOD." International Journal of Bifurcation and Chaos 11, no. 08 (August 2001): 2233–43. http://dx.doi.org/10.1142/s0218127401003310.

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In this letter, the impulsive feedback synchronization method is suggested. Synchronization condition is given by investigating the mechanism of the impulsive feedback synchronization. Furthermore, we consider the influences of noise and parameter mismatch since they inevitably exist in the practical experiment. Finally, a visual circuit implementation of impulsive feedback synchronization is performed. The research demonstrates that impulsive operator can spread frequency spectrum of chaotic solution. Impulsive feedback can synchronize chaotic systems and has the robustness to noise and parameter mismatch. It shows the potential application in chaotic communication.

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46

Zhang, Ke, and Xiao Ming Cao. "Inclination Errors Evaluation of Planar Lines with a Chaos Optimization." Applied Mechanics and Materials 37-38 (November 2010): 525–28. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.525.

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To improve inclination error evaluation of planar lines, chaos optimization is proposed to evaluate the minimum zone error in this paper. The evolutional optimum model and the calculation process are introduced. By using the properties of ergodicity, stochastic property, and “regularity” of chaos, the efficiency of chaos optimization algorithm (COA) is much higher than some stochastic algorithms such as simulated anneal algorithm (SAA) and genetic algorithm (GA) when COA is used to a kind of continuous problems. The chaos optimization algorithm can improve the efficiency of searching in the whole field by gradually shrinking the area of optimization variable. Finally, the control experiment results evaluated by different method such as the Least Square, Simplex search, Powell optimum methods and GA, indicate that the proposed method does provide better accuracy on inclination error evaluation.

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47

DANIELS, KAREN E., OLIVER BRAUSCH, WERNER PESCH, and EBERHARD BODENSCHATZ. "Competition and bistability of ordered undulations and undulation chaos in inclined layer convection." Journal of Fluid Mechanics 597 (February 1, 2008): 261–82. http://dx.doi.org/10.1017/s0022112007009615.

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Experimental and theoretical investigations of undulation patterns in high-pressure inclined layer gas convection at a Prandtl number near unity are reported. Particular focus is given to the competition between the spatiotemporal chaotic state of undulation chaos and stationary patterns of ordered undulations. In experiments, a competition and bistability between the two states is observed, with ordered undulations most prevalent at higher Rayleigh number. The spectral pattern entropy, spatial correlation lengths and defect statistics are used to characterize the competing states. The experiments are complemented by a theoretical analysis of the Oberbeck–Boussinesq equations. The stability region of the ordered undulations as a function of their wave vectors and the Rayleigh number is obtained with Galerkin techniques. In addition, direct numerical simulations are used to investigate the spatiotemporal dynamics. In the simulations, both ordered undulations and undulation chaos were observed dependent on initial conditions. Experiment and theory are found to agree well.

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48

Meissner, H., and G. Schmidt. "A simple experiment for studying the transition from order to chaos." American Journal of Physics 54, no. 9 (September 1986): 800–804. http://dx.doi.org/10.1119/1.14449.

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Evdokimov, Nikolai V., Vladimir P. Komolov, and Pavel V. Komolov. "Dynamic chaos interference in Hamiltonian systems: experiment and potential radiophysics applications." Physics-Uspekhi 44, no. 7 (July 31, 2001): 735–54. http://dx.doi.org/10.1070/pu2001v044n07abeh000861.

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Pinto, R. D., J. C. Sartorelli, and W. M. Gonçalves. "Homoclinic tangencies and routes to chaos in a dripping faucet experiment." Physica A: Statistical Mechanics and its Applications 291, no. 1-4 (March 2001): 244–54. http://dx.doi.org/10.1016/s0378-4371(00)00513-6.

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