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Relevant bibliographies by topics / Graph of discontinuous maps

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Journal articles

Academic literature on the topic 'Graph of discontinuous maps'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Graph of discontinuous maps"

1

Efremova, L. S., and E. N. Makhrova. "One-dimensional dynamical systems." Russian Mathematical Surveys 76, no. 5 (2021): 821–81. http://dx.doi.org/10.1070/rm9998.

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Abstract The survey is devoted to the topological dynamics of maps defined on one-dimensional continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or dendrites (locally connected continua without subsets homeomorphic to a circle). Connections between the periodic behaviour of trajectories, the existence of a horseshoe and homoclinic trajectories, and the positivity of topological entropy are investigated. Necessary and sufficient conditions for entropy chaos in continuous maps of an interval, a circle, or a finite graph, and sufficient conditions for entropy chaos in continuous maps of dendrites are presented. Reasons for similarities and differences between the properties of maps defined on the continua under consideration are analyzed. Extensions of Sharkovsky’s theorem to certain discontinuous maps of a line or an interval and continuous maps on a plane are considered. Bibliography: 207 titles.

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2

Li, Denghui, Zhenbang Cao, Xiaoming Zhang, Celso Grebogi, and Jianhua Xie. "Strange Nonchaotic Attractors From a Family of Quasiperiodically Forced Piecewise Linear Maps." International Journal of Bifurcation and Chaos 31, no. 07 (2021): 2150111. http://dx.doi.org/10.1142/s021812742150111x.

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In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally, to demonstrate and validate our theoretical results, numerical simulations are presented to exhibit the corresponding phase portrait and Lyapunov exponents portrait.

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3

Scott, C. B., and Eric Mjolsness. "Graph diffusion distance: Properties and efficient computation." PLOS ONE 16, no. 4 (2021): e0249624. http://dx.doi.org/10.1371/journal.pone.0249624.

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We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponential matrices, under norm-preserving and sparsity constraints. Variants of the distance metric are introduced to consider such optimized maps under sparsity constraints as well as fixed time-scaling between the two Laplacians. The objective function of this optimization is multimodal and has discontinuous slope, and is hence difficult for univariate optimizers to solve. We demonstrate a novel procedure for efficiently calculating these optima for two of our distance measure variants. We present numerical experiments demonstrating that (a) upper bounds of our distance metrics can be used to distinguish between lineages of related graphs; (b) our procedure is faster at finding the required optima, by as much as a factor of 103; and (c) the upper bounds satisfy the triangle inequality exactly under some assumptions and approximately under others. We also derive an upper bound for the distance between two graph products, in terms of the distance between the two pairs of factors. Additionally, we present several possible applications, including the construction of infinite “graph limits” by means of Cauchy sequences of graphs related to one another by our distance measure.

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4

ANDRES, JAN, PAVLA ŠNYRYCHOVÁ та PIOTR SZUCA. "SHARKOVSKII'S THEOREM FOR CONNECTIVITY Gδ-RELATIONS". International Journal of Bifurcation and Chaos 16, № 08 (2006): 2377–93. http://dx.doi.org/10.1142/s0218127406016136.

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A version of Sharkovskii's cycle coexistence theorem is formulated for a composition of connectivity Gδ-relations with closed values. Thus, a multivalued version in [Andres & Pastor, 2005] holding with at most two exceptions for M-maps, jointly with a single-valued version in [Szuca, 2003], for functions with a connectivity Gδ-graph, are generalized. In particular, our statement is applicable to differential inclusions as well as to some discontinuous functions.

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5

Margielewicz, J., J. Wojnarowski, and S. Zawiślak. "Numerical Studies of Nonlinear Gearing Models Using Bond Graph Method." International Journal of Applied Mechanics and Engineering 23, no. 4 (2018): 885–96. http://dx.doi.org/10.2478/ijame-2018-0049.

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Abstract The present paper is dedicated to computer simulations performed using a numerical model of a one-stage gear. The motion equations were derived utilizing the bond graph method. The formulated model takes into consideration the variable stiffness of toothings as well as an inter-tooth clearance which has been represented via discontinuous elements with so called dead zones. As a result of these assumptions, the nonlinear model was obtained which enables representation of the dynamic phenomena of the considered gear. In the paper, an influence of errors of gear wheels’ co-operation on the character of excited dynamic phenomena was studied. The methodology of the analyses consists in utilization of the following tools: color maps of distribution of the maximal Lapunov coefficient and bifurcation diagrams. Based upon them, the parameters were determined, for which the Poincare portrait represents a structure of the chaotic attractor. For the identified attractors, the initial attractors were calculated numerically - which along with the changes of the control parameters are subjected to multiplication, stretching or rotation.

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6

Bellettini, Giovanni, Alaa Elshorbagy, Maurizio Paolini, and Riccardo Scala. "On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 2 (2019): 445–77. http://dx.doi.org/10.1007/s10231-019-00887-0.

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7

Abello, James. "Hierarchical graph maps." Computers & Graphics 28, no. 3 (2004): 345–59. http://dx.doi.org/10.1016/j.cag.2004.03.012.

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8

Bazhenov, Viktor, Olha Pogorelova, and Tetiana Postnikova. "Transient Chaos in Platform-vibrator with Shock." Strength of Materials and Theory of Structures, no. 106 (May 24, 2021): 22–40. http://dx.doi.org/10.32347/2410-2547.2021.106.22-40.

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Platform-vibrator with shock is widely used in the construction industry for compacting and molding large concrete products. Its mathematical model, created in our previous work, meets all the basic requirements of shock-vibration technology for the precast concrete production on low-frequency resonant platform-vibrators. This model corresponds to the two-body 2-DOF vibro-impact system with a soft impact. It is strongly nonlinear non-smooth discontinuous system. This is unusual vibro-impact system due to its specific properties. The upper body, with a very large mass, breaks away from the lower body a very short distance, and then falls down onto the soft constraint that causes a soft impact. Then it bounces and falls again, and so on. A soft impact is simulated with nonlinear Hertzian contact force. This model exhibited many unique phenomena inherent in nonlinear non-smooth dynamical systems with varying control parameters. In this paper, we demonstrate the transient chaos in a vibro-impact system. Our finding of transient chaos in platform-vibrator with shock, besides being a remarkable phenomenon by itself, provides an understanding of the dynamical processes that occur in the platform-vibrator when varying the technological mass of the mold with concrete. Phase trajectories, Poincaré maps, graphs of time series and contact forces, Fourier spectra, the largest Lyapunov exponent, and wavelet characteristics are used in numerical investigations to determine the chaotic and periodic phases of the realization. We show both the dependence of the transient chaos on the control parameter value and the sensitive dependence on the initial conditions. We hope that this analysis can help avoid undesirable platform-vibrator behaviour during design and operation due to inappropriate system parameters, since transient chaos may be a dangerous and unwanted state of a vibro-impact system.

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9

Bischi, Gian-Italo, Laura Gardini, and Fabio Tramontana. "Bifurcation curves in discontinuous maps." Discrete & Continuous Dynamical Systems - B 13, no. 2 (2010): 249–67. http://dx.doi.org/10.3934/dcdsb.2010.13.249.

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10

Pavlovic, Branka. "Discontinuous Maps from Lipschitz Algebras." Journal of Functional Analysis 155, no. 2 (1998): 436–54. http://dx.doi.org/10.1006/jfan.1997.3232.

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