We are proudly a Ukrainian website. Our country was attacked by Russian Armed Forces on Feb. 24, 2022.
You can support the Ukrainian Army by following the link: https://u24.gov.ua/.
Even the smallest donation is hugely appreciated!
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Dynamical Systems.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Journal articles on the topic "Dynamical Systems":
1
Hornstein, John, and V. I. Arnold. "Dynamical Systems." American Mathematical Monthly 96, no. 9 (November 1989): 861. http://dx.doi.org/10.2307/2324864.
Chillingworth, D. R. J., D. K. Arrowsmith, and C. M. Place. "Dynamical Systems." Mathematical Gazette 79, no. 484 (March 1995): 233. http://dx.doi.org/10.2307/3620112.
Li, Zhiming, Minghan Wang, and Guo Wei. "Induced hyperspace dynamical systems of symbolic dynamical systems." International Journal of General Systems 47, no. 8 (October 3, 2018): 809–20. http://dx.doi.org/10.1080/03081079.2018.1524467.
Dynamical systems are ubiquitous in the physical world and are often well-described by partial differential equations (PDEs). Despite their formally infinite-dimensional solution space, a number of systems have long time dynamics that live on a low-dimensional manifold. However, current methods to probe the long time dynamics require prerequisite knowledge about the underlying dynamics of the system. In this study, we present a data-driven hybrid modeling approach to help tackle this problem by combining numerically derived representations and latent representations obtained from an autoencoder. We validate our latent representations and show they are dynamically interpretable, capturing the dynamical characteristics of qualitatively distinct solution types. Furthermore, we probe the topological preservation of the latent representation with respect to the raw dynamical data using methods from persistent homology. Finally, we show that our framework is generalizable, having been successfully applied to both integrable and non-integrable systems that capture a rich and diverse array of solution types. Our method does not require any prior dynamical knowledge of the system and can be used to discover the intrinsic dynamical behavior in a purely data-driven way.
8
Caballero, Rubén, Alexandre N. Carvalho, Pedro Marín-Rubio, and José Valero. "Robustness of dynamically gradient multivalued dynamical systems." Discrete & Continuous Dynamical Systems - B 24, no. 3 (2019): 1049–77. http://dx.doi.org/10.3934/dcdsb.2019006.
Landry, Nicholas W., and Juan G. Restrepo. "Hypergraph assortativity: A dynamical systems perspective." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 5 (May 2022): 053113. http://dx.doi.org/10.1063/5.0086905.
The largest eigenvalue of the matrix describing a network’s contact structure is often important in predicting the behavior of dynamical processes. We extend this notion to hypergraphs and motivate the importance of an analogous eigenvalue, the expansion eigenvalue, for hypergraph dynamical processes. Using a mean-field approach, we derive an approximation to the expansion eigenvalue in terms of the degree sequence for uncorrelated hypergraphs. We introduce a generative model for hypergraphs that includes degree assortativity, and use a perturbation approach to derive an approximation to the expansion eigenvalue for assortative hypergraphs. We define the dynamical assortativity, a dynamically sensible definition of assortativity for uniform hypergraphs, and describe how reducing the dynamical assortativity of hypergraphs through preferential rewiring can extinguish epidemics. We validate our results with both synthetic and empirical datasets.
10
Akashi, Shigeo. "Embedding of expansive dynamical systems into symbolic dynamical systems." Reports on Mathematical Physics 46, no. 1-2 (August 2000): 11–14. http://dx.doi.org/10.1016/s0034-4877(01)80003-3.
Dissertations / Theses on the topic "Dynamical Systems":
1
Behrisch, Mike, Sebastian Kerkhoff, Reinhard Pöschel, Friedrich Martin Schneider, and Stefan Siegmund. "Dynamical Systems in Categories." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-129909.
In this article we establish a bridge between dynamical systems, including topological and measurable dynamical systems as well as continuous skew product flows and nonautonomous dynamical systems; and coalgebras in categories having all finite products. We introduce a straightforward unifying definition of abstract dynamical system on finite product categories. Furthermore, we prove that such systems are in a unique correspondence with monadic algebras whose signature functor takes products with the time space. We substantiate that the categories of topological spaces, metrisable and uniformisable spaces have exponential objects w.r.t. locally compact Hausdorff, σ-compact or arbitrary time spaces as exponents, respectively. Exploiting the adjunction between taking products and exponential objects, we demonstrate a one-to-one correspondence between monadic algebras (given by dynamical systems) for the left-adjoint functor and comonadic coalgebras for the other. This, finally, provides a new, alternative perspective on dynamical systems.
Part A. We prove existence of smooth invariant circles for area preserving twist maps close enough to integrable using renormalisation. The smoothness depends upon that of the map and the Liouville exponent of the rotation number. Part B. Ruelle and Capocaccia gave a new definition of Gibbs states on Smale spaces. Equilibrium states of suitable function there on are known to be Gibbs states. The converse in discussed in this paper, where the problem is reduced to shift spaces and there solved by constructing suitable conjugating homeomorphisms in order to verify the conditions for Gibbs states which Bowen gave for shift spaces, where the equivalence to equilibrium states is known. Part C. On subshifts which are derived from Markov partitions exists an equivalence relation which idendifies points that lie on the boundary set of the partition. In this paper we restrict to symbolic dynamics. We express the quotient space in terms of a non-transitive subshift of finite type, give a necessary and sufficient condition for the existence of a local product structure and evaluate the Zeta function of the quotient space. Finally we give an example where the quotient space is again a subshift of finite type.
4
Miles, Richard Craig. "Arithmetic dynamical systems." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323222.
In this work, we look at the dynamics of four different spaces, the interval, the unit circle, subshifts of finite type and compact countable sets. We put our emphasis on chaotic dynamical system and exhibit sufficient conditions for the system on the interval, the unit circle and subshifts of finite type to be chaotic in three different types of chaos. On the interval, we reveal two weak conditions’s role as a fast track to chaotic behavior. We also explain how a strong dense periodicity property influences chaotic behavior of dynamics on the interval, the unit circle and subshifts of finite type. Finally we show how dynamics property of compact countable sets effecting the structure of the sets.
6
Hillman, Chris. "Sturmian dynamical systems /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5806.
This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems commonly arising in system identi cation are model instability (e.g. unreliability of long-term, open-loop predictions), and nonconvexity of quality-of- t criteria, such as simulation error (a.k.a. output error). To address these problems, this thesis presents convex parametrizations of stable dynamical systems, convex quality-of- t criteria, and e cient algorithms to optimize the latter over the former. In particular, this thesis makes extensive use of Lagrangian relaxation, a technique for generating convex approximations to nonconvex optimization problems. Recently, Lagrangian relaxation has been used to approximate simulation error and guarantee nonlinear model stability via semide nite programming (SDP), however, the resulting SDPs have large dimension, limiting their practical utility. The rst contribution of this thesis is a custom interior point algorithm that exploits structure in the problem to signi cantly reduce computational complexity. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, in which superior generalization to new data is demonstrated. Equipped with this algorithmic machinery, the second contribution of this thesis is the incorporation of model stability constraints into the maximum likelihood framework. Speci - cally, Lagrangian relaxation is combined with the expectation maximization (EM) algorithm to derive tight bounds on the likelihood function, that can be optimized over a convex parametrization of all stable linear dynamical systems. Two di erent formulations are presented, one of which gives higher delity bounds when disturbances (a.k.a. process noise) dominate measurement noise, and vice versa. Finally, identi cation of positive systems is considered. Such systems enjoy substantially simpler stability and performance analysis compared to the general linear time-invariant iv Abstract (LTI) case, and appear frequently in applications where physical constraints imply nonnegativity of the quantities of interest. Lagrangian relaxation is used to derive new convex parametrizations of stable positive systems and quality-of- t criteria, and substantial improvements in accuracy of the identi ed models, compared to existing approaches based on weighted equation error, are demonstrated. Furthermore, the convex parametrizations of stable systems based on linear Lyapunov functions are shown to be amenable to distributed optimization, which is useful for identi cation of large-scale networked dynamical systems.
8
Freeman, Isaac. "A modular system for constructing dynamical systems." Thesis, University of Canterbury. Mathematics, 1998. http://hdl.handle.net/10092/8888.
This thesis discusses a method based on the dual principle of Rössler, and developed by Deng, for systematically constructing robust dynamical systems from lower dimensional subsystems. Systems built using this method may be modified easily, and are suitable for mathematical modelling. Extensions are made to this scheme, which allow one to describe a wider range of dynamical behaviour. These extensions allow the creation of systems that reproduce qualitative features of the Lorenz Attractor (including bifurcation properties) and of Chua's circuit, but which are easily extensible.
9
Ozaki, Junichi. "Dynamical quantum effects in cluster dynamics of Fermi systems." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199083.
CAPPELLINI, VALERIO. "QUANTUM DYNAMICAL ENTROPIES AND COMPLEXITY IN DYNAMICAL SYSTEMS." Doctoral thesis, Università degli studi di Trieste, 2004. http://thesis2.sba.units.it/store/handle/item/12545.
2002/2003 We analyze the behavior of two quantum dynamical entropies in
connection with the classical limit. Using strongly chaotic
classical dynamical systems as models (Arnold Cat Maps and Sawtooth
Maps), we also propose a discretization procedure that resembles
quantization; even in this case, studies of quantum dynamical entropy
production are carried out and the connection with the continuous
limit is explored. In both case (quantization and discretization) the
entropy production converge to the Kolmogorov-Sinai invariant on
time-scales that are logarithmic in the quantization (discretization)
parameter. XVI Ciclo 1969 Versione digitalizzata della tesi di dottorato cartacea.
Arnold, Ludwig, Christopher K. R. T. Jones, Konstantin Mischaikow, and Geneviève Raugel. Dynamical Systems. Edited by Russell Johnson. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0095237.
Kurzhanski, Alexander B., and Karl Sigmund, eds. Dynamical Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-662-00748-8.
McLennan, Andrew. "Dynamical Systems." In Advanced Fixed Point Theory for Economics, 289–330. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0710-2_15.
Neimark, Juri I. "Dynamical systems." In Foundations of Engineering Mechanics, 5–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-47878-2_2.
Michel, Anthony N., Ling Hou, and Derong Liu. "Dynamical Systems." In Systems & Control: Foundations & Applications, 19–76. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15275-2_2.
Bhatia, Nam Parshad, and George Philip Szegö. "Dynamical Systems." In Stability Theory of Dynamical Systems, 5–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-62006-5_2.
Polderman, Jan Willem, and Jan C. Willems. "Dynamical Systems." In Texts in Applied Mathematics, 1–25. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4757-2953-5_1.
Bubnicki, Zdzislaw. "Dynamical Systems." In Analysis and Decision Making in Uncertain Systems, 169–200. London: Springer London, 2004. http://dx.doi.org/10.1007/978-1-4471-3760-3_8.
Everest, Graham, and Thomas Ward. "Dynamical Systems." In Heights of Polynomials and Entropy in Algebraic Dynamics, 29–50. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-3898-3_2.
Conference papers on the topic "Dynamical Systems":
1
Jiang, Yunping, and Lan Wen. "DYNAMICAL SYSTEMS." In Proceedings of the International Conference in Honor of Professor Liao Shantao. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814527002.
Andersson, Stig I., Ǻke E. Andersson, and Ulf Ottoson. "Dynamical Systems." In Conference. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814535526.
Shan-Tao, Liao, Ye Yan-Qian, and Ding Tong-Ren. "Dynamical Systems." In Special Program at Nankai Institute of Mathematics. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814535892.
Boutayeb, M. "A decentralized software sensor based approach for large-scale dynamical systems." In 2010 4th Annual IEEE Systems Conference. IEEE, 2010. http://dx.doi.org/10.1109/systems.2010.5482344.
Chen, Wenchao, Bo Chen, Yicheng Liu, Qianru Zhao, and Mingyuan Zhou. "Switching Poisson Gamma Dynamical Systems." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/281.
We propose Switching Poisson gamma dynamical systems (SPGDS) to model sequentially observed multivariate count data. Different from previous models, SPGDS assigns its latent variables into mixture of gamma distributed parameters to model complex sequences and describe the nonlinear dynamics, meanwhile, capture various temporal dependencies. For efficient inference, we develop a scalable hybrid stochastic gradient-MCMC and switching recurrent autoencoding variational inference, which is scalable to large scale sequences and fast in out-of-sample prediction. Experiments on both unsupervised and supervised tasks demonstrate that the proposed model not only has excellent fitting and prediction performance on complex dynamic sequences, but also separates different dynamical patterns within them.
7
Rabinovich, Y., A. Sinclair, and A. Wigderson. "Quadratic dynamical systems." In Proceedings., 33rd Annual Symposium on Foundations of Computer Science. IEEE, 1992. http://dx.doi.org/10.1109/sfcs.1992.267761.
Pokorny, Pavel. "Excitable dynamical systems." In 12th Czech-Slovak-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, edited by Jan Perina, Sr., Miroslav Hrabovsky, and Jaromir Krepelka. SPIE, 2001. http://dx.doi.org/10.1117/12.417864.
YOUNG, LAI-SANG. "DYNAMICAL SYSTEMS EVOLVING." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0035.
Hale, Jack K. Analysis of Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, August 1988. http://dx.doi.org/10.21236/ada204636.
Jones, Christopher, Steven Wiggins, and George Haller. Dynamical Systems and Oceanography. Fort Belvoir, VA: Defense Technical Information Center, April 1994. http://dx.doi.org/10.21236/ada279807.
Jones, Christopher, Steven Wiggins, and George Haller. Dynamical Systems and Oceanography. Fort Belvoir, VA: Defense Technical Information Center, April 1994. http://dx.doi.org/10.21236/ada282635.
Hale, Jack K. Analysis of Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, December 1985. http://dx.doi.org/10.21236/ada166224.
Weerasinghe, Ananda P. Controlled Stochastic Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, April 2007. http://dx.doi.org/10.21236/ada470046.
Philip Holmes. NONLINEAR DYNAMICAL SYSTEMS - Final report. Office of Scientific and Technical Information (OSTI), December 2005. http://dx.doi.org/10.2172/888778.
Denman, Matthew R., and Arlo Leroy Ames. Dynamical systems probabilistic risk assessment. Office of Scientific and Technical Information (OSTI), March 2014. http://dx.doi.org/10.2172/1177044.
Barbone, Paul E. Shock Survivability of Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, May 1999. http://dx.doi.org/10.21236/ada363045.
Glinsky, Michael Edwin, and Poul Hjorth. Helicity in Hamiltonian dynamical systems. Office of Scientific and Technical Information (OSTI), December 2019. http://dx.doi.org/10.2172/1595915.
