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Relevant bibliographies by topics / Dynamical chaos

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Academic literature on the topic 'Dynamical chaos'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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Journal articles on the topic "Dynamical chaos"

1

Brandon, John, and Edward Ott. "Chaos in Dynamical Systems." Mathematical Gazette 79, no. 484 (March 1995): 233. http://dx.doi.org/10.2307/3620113.

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Bohn, John L. "Chaos and Dynamical Systems." American Journal of Physics 88, no. 4 (April 2020): 335–36. http://dx.doi.org/10.1119/10.0000678.

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Chandra Bag, Bidhan, and Deb Shankar Ray. "Environment-induced dynamical chaos." Physical Review E 62, no. 3 (September 1, 2000): 4409–12. http://dx.doi.org/10.1103/physreve.62.4409.

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Ott, Edward, and Kurt Wiesenfeld. "Chaos in Dynamical Systems." Physics Today 47, no. 1 (January 1994): 45. http://dx.doi.org/10.1063/1.2808369.

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Casati, Giulio, and Davide Rossini. "Dynamical Chaos and Decoherence." Progress of Theoretical Physics Supplement 166 (2007): 70–84. http://dx.doi.org/10.1143/ptps.166.70.

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Rota, Gian-Carlo. "Dynamical systems and chaos." Advances in Mathematics 56, no. 3 (June 1985): 319. http://dx.doi.org/10.1016/0001-8708(85)90042-8.

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Hastings, Alan. "Chaos in dynamical systems." Bulletin of Mathematical Biology 57, no. 6 (November 1995): 943–44. http://dx.doi.org/10.1007/bf02458303.

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Martínez-Giménez, Félix, Alfred Peris, and Francisco Rodenas. "Chaos on Fuzzy Dynamical Systems." Mathematics 9, no. 20 (October 18, 2021): 2629. http://dx.doi.org/10.3390/math9202629.

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Given a continuous map f:X→X on a metric space, it induces the maps f¯:K(X)→K(X), on the hyperspace of nonempty compact subspaces of X, and f^:F(X)→F(X), on the space of normal fuzzy sets, consisting of the upper semicontinuous functions u:X→[0,1] with compact support. Each of these spaces can be endowed with a respective metric. In this work, we studied the relationships among the dynamical systems (X,f), (K(X),f¯), and (F(X),f^). In particular, we considered several dynamical properties related to chaos: Devaney chaos, A-transitivity, Li–Yorke chaos, and distributional chaos, extending some results in work by Jardón, Sánchez and Sanchis (Mathematics 2020, 8, 1862) and work by Bernardes, Peris and Rodenas (Integr. Equ. Oper. Theory 2017, 88, 451–463). Especial attention is given to the dynamics of (continuous and linear) operators on metrizable topological vector spaces (linear dynamics).

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BROWN, RAY, ROBERT BEREZDIVIN, and LEON O. CHUA. "CHAOS AND COMPLEXITY." International Journal of Bifurcation and Chaos 11, no. 01 (January 2001): 19–26. http://dx.doi.org/10.1142/s0218127401001992.

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In this paper we show how to relate a form of high-dimensional complexity to chaotic and other types of dynamical systems. The derivation shows how "near-chaotic" complexity can arise without the presence of homoclinic tangles or positive Lyapunov exponents. The relationship we derive follows from the observation that the elements of invariant finite integer lattices of high-dimensional dynamical systems can, themselves, be viewed as single integers rather than coordinates of a point in n-space. From this observation it is possible to construct high-dimensional dynamical systems which have properties of shifts but for which there is no conventional topological conjugacy to a shift. The particular manner in which the shift appears in high-dimensional dynamical systems suggests that some forms of complexity arise from the presence of chaotic dynamics which are obscured by the large dimensionality of the system domain.

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Inoue, Kei. "Analysis of Chaotic Dynamics by the Extended Entropic Chaos Degree." Entropy 24, no. 6 (June 14, 2022): 827. http://dx.doi.org/10.3390/e24060827.

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The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics.

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Dissertations / Theses on the topic "Dynamical chaos"

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Krcelic, Khristine M. "Chaos and Dynamical Systems." Youngstown State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1364545282.

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Bird, C. M. "The control of chaos." Thesis, University of Surrey, 1996. http://epubs.surrey.ac.uk/804952/.

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Chygryn, S. A. "Intermittent chaos in Hamiltonian dynamical systems." Thesis, Сумський державний університет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/35109.

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The statistical characterization of chaotic trajectories in Hamiltonian dynamical systems attract special interest. Such systems usually show coexistence of regions of chaotic and regular motion in the phase space. When chaotic trajectories approach the regular regions, they stick to their border inducing long periods of almost regular motion. This intermittent behavior determines the main dynamical properties of the system. The fundamental problem is how to quantitatively relate the intermittency of the chaotic dynamics to the distribution and stability properties of the regular regions of the phase space. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35109

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Ruiter, Julia. "Practical Chaos: Using Dynamical Systems to Encrypt Audio and Visual Data." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/scripps_theses/1389.

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Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

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Orrell, D. J. "Modelling nonlinear dynamical systems : chaos, uncertainty and error." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393997.

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Wilson, Howard B. "Applications of dynamical systems in ecology." Thesis, University of Warwick, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387403.

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Beale, L. C. "Chaos, strange attractors and bifurcations in dissipative dynamical systems." Thesis, University of Canterbury. Mathematics, 1988. http://hdl.handle.net/10092/8410.

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In this dissertation a study is made of chaotic behaviour, the bifurcation sequences leading to chaos and the manifestation of chaos in the form of a strange attractor in dissipative dynamical systems. In chapter 1 we provide an overview of the material covered in this review and introduce several concepts from the basic theory of dynamical systems, such as Poincaré return maps and simple bifurcations. After introducing the concept of chaos and strange attractors in dissipative dynamical systems, we divide higher dimensional systems into three categories in chapter 2. Each is illustrated with examples. Central to the discussion is the well studied Lorenz system. Other important mathematical models are looked at, in particular the Rössler model and the two-dimensional Hénon map. The various measures of dimension, in the fractal context, and the numerical methods currently in use for determining these quantities are presented in chapter 3. In view of their relative computational simplicity and direct relevance to chaos, one-dimensional mappings are looked at in chapter 4. In chapter 5, the idea of the transition to turbulence being a chaotic regime is introduced and the various routes to turbulence are examined in turn. In chapter 6, we present a Fourier series method for approximating the phase-space trajectories of a dynamical system. We illustrate the technique by carrying out the calculations required on the equations describing the evolution of the spherical pendulum model of Miles (l984b). No attempt is made to cover the whole field of research chaos. The use of symbolic dynamics is avoided wherever possible for simplicity and brevity in this review.

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Siegwart, David Kevin. "Classical and quantum chaos of dynamical systems : rotating billiards." Thesis, Durham University, 1990. http://etheses.dur.ac.uk/6228/.

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The theory of classical chaos is reviewed. From the definition of integrable systems using the Hamilton-Jacobi equation, the theory of perturbed systems is developed and the Kolmogorov-Arnold-Moser (KAM) theorem is explained. It is shown how chaotic motion in Hamiltonian systems is governed by the in tricate connections of stable and unstable invariant manifolds, and how it can be catagorised by algorithmic complexity and symbolic dynamics, giving chaotic measures such as Lyapunov exponents and Kolmogorov entropy. Also reviewed is Gutzwiller's semiclassical trace formula for strongly chaotic systems, torus quantisation for integrable systems, the asymptotic level density for stationary billiards, and random matrix theories for describing spectral fluctuation properties. The classical theory is applied to rotating billiards, particularly the free motion of a particle in a circular billiard rotating uniformly in its own plane about a point on its edge. Numerically, it is shown that the system's classical behaviour ranges from fully chaotic at intermediate energies, to completely integrable at very low and very high energies. It is shown that the strong chaos is due to discontinuities in the Poincare map, caused by trajectories which just glance the boundary-an effect of the curvature of trajectories. Weaker chaos exists due to the usual folding and stretching of the Hamiltonian flow. Approximate invariant curves for integrable motion are found, valid far from the presence of glancing trajectories. The major structures of phase space are investigated: a fixed point and its bifurcation into a two-cycle, and their stabilities. Lyapunov exponents for trajectories are calculated and the chaotic volume for a wide range of energies is measured. Quantum mechanically, the energy spectrum of the system is found numerically. It is shown that at the energies where the classical system is completely integrable the levels do not repel, and at those energies where it is completely chaotic there is strong level repulsion. The nearest neighbour level spacing distributions for various ranges of energy and values of Planck's constant are found. In the semiclassical limit, it is shown that, for energies where the classical system is completely chaotic, the level spacing statistics are Wigner, and where it is completely integrable, the level spacing statistics are Poisson. A model is described for the spacing distributions where the levels can be either Wigner or Poisson, which is useful for showing the transition from one to the other, and ad equately describes the statistics. Theoretically, the asymptotic level density for rotating billiards is calculated, and this is compared with the numerical results with good agreement, after modification of the method to include all levels.

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Tesař, Lukáš. "Nelineární dynamické systémy a chaos." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-392844.

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The diploma thesis deals with nonlinear dynamical systems with emphasis on typical phenomena like bifurcation or chaotic behavior. The basic theoretical knowledge is applied to analysis of selected (chaotic) models, namely, Lorenz, Rössler and Chen system. The practical part of the work is then focused on a numerical simulation to confirm the correctness of the theoretical results. In particular, an algorithm for calculating the largest Lyapunov exponent is created (under the MATLAB environment). It represents the main tool for indicating chaos in a system.

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Kateregga, George William. "Bifurcations in a chaotic dynamical system." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401527.

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Dynamical systems possess an interesting and complex behaviour that have attracted a number of researchers across different fields, such as Biology, Economics and most importantly in Engineering. The complex and unpredictability of nonlinear customary behaviour or the chaotic behaviour, makes it strange to analyse them. This thesis presents the analysis of the system of nonlinear differential equations of the so--called Lu--Chen--Cheng system. The system has similar dynamical behaviour with the famous Lorenz system. The nature of equilibrium points and stability of the system is presented in the thesis. Examples of chaotic dynamical systems are presented in the theory. The thesis shows the dynamical structure of the Lu--Chen--Cheng system depending on the particular values of the system parameters and routes to chaos. This is done by both the qualitative and numerical techniques. The bifurcation diagrams of the Lu--Chen--Cheng system that indicate limit cycles and chaos as one parameter is varied are shown with the help of the largest Lyapunov exponent, which also confirms chaos in the system. It is found out that most of the system's equilibria are unstable especially for positive values of the parameters $a, b$. It is observed that the system is highly sensitive to initial conditions. This study is very important because, it supports the previous findings on chaotic behaviours of different dynamical systems.

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Books on the topic "Dynamical chaos"

1

Anishchenko, V. S. Dynamical chaos, basic concepts. Leipzig: Teubner, 1987.

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Floris, Takens, ed. Dynamical systems and chaos. New York: Springer, 2011.

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Broer, Henk, and Floris Takens. Dynamical Systems and Chaos. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6870-8.

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Chaos in dynamical systems. 2nd ed. Cambridge, U.K: Cambridge University Press, 2002.

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Anishchenko, V. S. Dynamical chaos: Basic concepts. Leipzig: Teubner Verlagsgellschaft, 1987.

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Ott, Edward. Chaos in dynamical systems. Cambridge [England]: Cambridge University Press, 1993.

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Robinson, Clark. Dynamical systems: Stability, symbolic dynamics, and chaos. Boca Raton, Fla: CRC Press, 1995.

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Robinson, Clark. Dynamical systems: Stability, symbolic dynamics, and chaos. 2nd ed. Boca Raton, Fla: CRC Press, 1999.

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Dynamical systems: Stability, symbolic dynamics, and chaos. Boca Raton: CRC Press, 1995.

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Dynamical systems: Stability, symbolic dynamics, and chaos. 2nd ed. Boca Raton, Fla: CRC Press, 1999.

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Book chapters on the topic "Dynamical chaos"

1

Sivaprakasam, Siva, and Cristina Masoller Ottieri. "Chaos Synchronization." In Unlocking Dynamical Diversity, 185–215. Chichester, UK: John Wiley & Sons, Ltd, 2005. http://dx.doi.org/10.1002/0470856211.ch6.

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Kuznetsov, Sergey P. "Dynamical Systems and Hyperbolicity." In Hyperbolic Chaos, 3–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23666-2_1.

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Devaney, Robert L. "Chaos." In An Introduction to Chaotic Dynamical Systems, 61–66. 3rd ed. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9780429280801-8.

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Kapitaniak, Tomasz. "Continuous Dynamical Systems." In Chaos for Engineers, 5–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57143-5_2.

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Kapitaniak, Tomasz. "Discrete Dynamical Systems." In Chaos for Engineers, 39–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57143-5_3.

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Kapitaniak, Tomasz. "Continuous Dynamical Systems." In Chaos for Engineers, 5–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-97719-0_2.

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Kapitaniak, Tomasz. "Discrete Dynamical Systems." In Chaos for Engineers, 39–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-97719-0_3.

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Layek, G. c. "Chaos." In An Introduction to Dynamical Systems and Chaos, 497–574. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2556-0_12.

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Allie, Stuart, Alistair Mees, Kevin Judd, and Dave Watson. "Triangulating Noisy Dynamical Systems." In Control and Chaos, 1–11. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2446-4_1.

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Majumdar, Mukul, and Tapan Mitra. "Dynamical Systems: A Tutorial." In Optimization and Chaos, 1–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04060-7_1.

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Conference papers on the topic "Dynamical chaos"

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Siefert, M. "How to differentiate quantitatively between nonlinear dynamics, dynamical noise and measurement noise." In EXPERIMENTAL CHAOS: 8th Experimental Chaos Conference. AIP, 2004. http://dx.doi.org/10.1063/1.1846495.

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Scholz-Reiter, Bernd. "A Dynamical Approach for Modelling and Control of Production Systems." In EXPERIMENTAL CHAOS: 6th Experimental Chaos Conference. AIP, 2002. http://dx.doi.org/10.1063/1.1487535.

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Kittel, Achim. "Uncovering Characteristic Quantities from Chaotic Time Series Distorted by Dynamical Noise." In EXPERIMENTAL CHAOS: 7th Experimental Chaos Conference. AIP, 2003. http://dx.doi.org/10.1063/1.1612277.

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Otsuka, Kenju. "Modal Interference and Dynamical Instability in a Solid-State Slice Laser with Asymmetric End-Pumping." In EXPERIMENTAL CHAOS: 7th Experimental Chaos Conference. AIP, 2003. http://dx.doi.org/10.1063/1.1612202.

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BALL, ROWENA, and PHILIP HOLMES. "DYNAMICAL SYSTEMS, STABILITY, AND CHAOS." In Proceedings of the COSNet/CSIRO Workshop on Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812771025_0001.

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GAILEY, PAUL C., LEE M. HIVELY, and VLADIMIR A. PROTOPOPESCU. "ROBUST DETECTION OF DYNAMICAL CHANGE IN SCALP EEG." In 5th Experimental Chaos Conference. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811516_0017.

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Kapitaniak, Tomasz, and John Brindley. "Chaos and Nonlinear Mechanics." In Euromech Colloquim 308 “Chaos and Noise in Dynamical Systems”. WORLD SCIENTIFIC, 1994. http://dx.doi.org/10.1142/9789812798824.

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Gauthier, Daniel. "Controlling chaos in fast dynamical systems." In Frontiers in Optics. Washington, D.C.: OSA, 2003. http://dx.doi.org/10.1364/fio.2003.wq1.

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Stewart, H. Bruce. "Chaos, dynamical structure, and climate variability." In Introduction to chaos and the changing nature of science and medicine. AIP, 1996. http://dx.doi.org/10.1063/1.51063.

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GASPARD, PIERRE. "DYNAMICAL CHAOS AND NONEQUILIBRIUM STATISTICAL MECHANICS." In Proceedings of the International Conference on Fundamental Sciences: Mathematics and Theoretical Physics. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811264_0018.

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Reports on the topic "Dynamical chaos"

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Stewart, H. B. Chaos, dynamical structure and climate variability. Office of Scientific and Technical Information (OSTI), September 1995. http://dx.doi.org/10.2172/102163.

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Harrison, Robert G. Dynamical Instabilities, Chaos And Spatial Complexity In Fundamental Nonlinear Optical Interactions. Fort Belvoir, VA: Defense Technical Information Center, May 1994. http://dx.doi.org/10.21236/ada291223.

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JAMES, DANIEL F. DYNAMICAL STABILITY AND QUANTUM CHAOS OF IONS IN A LINEAR TRAP (1999002ER). Office of Scientific and Technical Information (OSTI), September 2002. http://dx.doi.org/10.2172/801242.

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Schmidt, G. Investigations of transitions from order to chaos in dynamical systems. Annual progress report. Office of Scientific and Technical Information (OSTI), March 1993. http://dx.doi.org/10.2172/10157816.

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Meiss, J. D., P. J. Morrison, and J. Tennyson. Summary of the 1991 ACP Workshop on Coherence and Chaos in Complex Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, September 1991. http://dx.doi.org/10.21236/ada243226.

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Schmidt, G. Investigation of transitions from order to chaos in dynamical systems. Final technical report, period ending May 31, 1996. Office of Scientific and Technical Information (OSTI), December 1996. http://dx.doi.org/10.2172/639743.

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Perdigão, Rui A. P. New Horizons of Predictability in Complex Dynamical Systems: From Fundamental Physics to Climate and Society. Meteoceanics, October 2021. http://dx.doi.org/10.46337/211021.

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Discerning the dynamics of complex systems in a mathematically rigorous and physically consistent manner is as fascinating as intimidating of a challenge, stirring deeply and intrinsically with the most fundamental Physics, while at the same time percolating through the deepest meanders of quotidian life. The socio-natural coevolution in climate dynamics is an example of that, exhibiting a striking articulation between governing principles and free will, in a stochastic-dynamic resonance that goes way beyond a reductionist dichotomy between cosmos and chaos. Subjacent to the conceptual and operational interdisciplinarity of that challenge, lies the simple formal elegance of a lingua franca for communication with Nature. This emerges from the innermost mathematical core of the Physics of Coevolutionary Complex Systems, articulating the wealth of insights and flavours from frontier natural, social and technical sciences in a coherent, integrated manner. Communicating thus with Nature, we equip ourselves with formal tools to better appreciate and discern complexity, by deciphering a synergistic codex underlying its emergence and dynamics. Thereby opening new pathways to see the “invisible” and predict the “unpredictable” – including relative to emergent non-recurrent phenomena such as irreversible transformations and extreme geophysical events in a changing climate. Frontier advances will be shared pertaining a dynamic that translates not only the formal, aesthetical and functional beauty of the Physics of Coevolutionary Complex Systems, but also enables and capacitates the analysis, modelling and decision support in crucial matters for the environment and society. By taking our emerging Physics in an optic of operational empowerment, some of our pioneering advances will be addressed such as the intelligence system Earth System Dynamic Intelligence and the Meteoceanics QITES Constellation, at the interface between frontier non-linear dynamics and emerging quantum technologies, to take the pulse of our planet, including in the detection and early warning of extreme geophysical events from Space.

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Schmidt, G. Investigations of transitions from order to chaos in dynamical systems. [Dept. of Physics/Engineering Physics, Stevens Inst. of Technology, Hoboken, New Jersey]. Office of Scientific and Technical Information (OSTI), March 1993. http://dx.doi.org/10.2172/6367445.

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Battaglini, Marco. Chaos and Unpredictability in Dynamic Social Problems. Cambridge, MA: National Bureau of Economic Research, January 2021. http://dx.doi.org/10.3386/w28347.

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Oh, Y. G., N. Sreenath, P. S. Krishnaprasad, and J. E. Marsden. The Dynamics of Coupled Planar Rigid Bodies. Part 2. Bifurcations, Periodic Solutions, and Chaos. Fort Belvoir, VA: Defense Technical Information Center, January 1988. http://dx.doi.org/10.21236/ada452393.

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