Relevant bibliographies by topics / Piecewise linear map

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Piecewise linear map'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Piecewise linear map"

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White,, Marvin S., and Patricia Griffin. "Piecewise Linear Rubber-Sheet Map Transformation." American Cartographer 12, no. 2 (January 1985): 123–31. http://dx.doi.org/10.1559/152304085783915135.

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BAILLIF, MATHIEU, and ANDRÉ DE CARVALHO. "PIECEWISE LINEAR MODEL FOR TREE MAPS." International Journal of Bifurcation and Chaos 11, no. 12 (December 2001): 3163–69. http://dx.doi.org/10.1142/s0218127401004108.

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We generalize to tree maps the theorems of Parry and Milnor–Thurston about the semi-conjugacy of a continuous piecewise monotone map f to a continuous piecewise linear map with constant slope, equal to the exponential of the entropy of f.
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Begun, Nikita, Pavel Kravetc, and Dmitrii Rachinskii. "Chaos in Saw Map." International Journal of Bifurcation and Chaos 29, no. 02 (February 2019): 1930005. http://dx.doi.org/10.1142/s0218127419300052.

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We consider the dynamics of a scalar piecewise linear “saw map” with infinitely many linear segments. In particular, such maps are generated as a Poincaré map of simple two-dimensional discrete time piecewise linear systems involving a saturation function. Alternatively, these systems can be viewed as a feedback loop with the so-called stop hysteresis operator. We analyze chaotic sets and attractors of the “saw map” depending on its parameters.
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KOLLÁR, LÁSZLÓ E., GÁBOR STÉPÁN, and JÁNOS TURI. "DYNAMICS OF PIECEWISE LINEAR DISCONTINUOUS MAPS." International Journal of Bifurcation and Chaos 14, no. 07 (July 2004): 2341–51. http://dx.doi.org/10.1142/s0218127404010837.

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In this paper, the dynamics of maps representing classes of controlled sampled systems with backlash are examined. First, a bilinear one-dimensional map is considered, and the analysis shows that, depending on the value of the control parameter, all orbits originating in an attractive set are either periodic or dense on the attractor. Moreover, the dense orbits have sensitive dependence on initial data, but behave rather regularly, i.e. they have quasiperiodic subsequences and the Lyapunov exponent of every orbit is zero. The inclusion of a second parameter, the processing delay, in the model leads to a piecewise linear two-dimensional map. The dynamics of this map are studied using numerical simulations which indicate similar behavior as in the one-dimensional case.
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Roberts, John A. G., Asaki Saito, and Franco Vivaldi. "Critical curves of a piecewise linear map." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 7 (July 2021): 073134. http://dx.doi.org/10.1063/5.0054334.

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Zhusubaliyev, Z. T., D. S. Kuzmina, and O. O. Yanochkina. "Bifurcation Analysis of Piecewise Smooth Bimodal Maps Using Normal Form." Proceedings of the Southwest State University 24, no. 3 (December 6, 2020): 137–51. http://dx.doi.org/10.21869/2223-1560-2020-24-3-137-151.

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Purpose of reseach. Studyof bifurcations in piecewise-smooth bimodal maps using a piecewise-linear continuous map as a normal form. Methods. We propose a technique for determining the parameters of a normal form based on the linearization of a piecewise-smooth map in a neighborhood of a critical fixed point. Results. The stability region of a fixed point is constructed numerically and analytically on the parameter plane. It is shown that this region is limited by two bifurcation curves: the lines of the classical period-doubling bifurcation and the “border collision” bifurcation. It is proposed a method for determining the parameters of a normal form as a function of the parameters of a piecewise smooth map. The analysis of "border-collision" bifurcations using piecewise-linear normal form is carried out. Conclusion. A bifurcation analysis of a piecewise-smooth irreversible bimodal map of the class Z1–Z3–Z1 modeling the dynamics of a pulse–modulated control system is carried out. It is proposed a technique for calculating the parameters of a piecewise linear continuous map used as a normal form. The main bifurcation transitions are calculated when leaving the stability region, both using the initial map and a piecewise linear normal form. The topological equivalence of these maps is numerically proved, indicating the reliability of the results of calculating the parameters of the normal form.
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Wang, Bin, Shihua Zhou, Changjun Zhou, and Xuedong Zheng. "A Novel Joint for Image Encryption and Coding Using Piecewise Linear Chaotic Map." Journal of Computational and Theoretical Nanoscience 13, no. 10 (October 1, 2016): 7137–43. http://dx.doi.org/10.1166/jctn.2016.5683.

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Due to the features of chaotic maps, they are widely used into encrypting and coding information. Inspired by the tent map which is used to code and encrypt binary data, a novel joint for image encryption and coding based on piecewise linear chaotic map is proposed in this paper. We divide piecewise linear chaotic map into 256 parts according to the property of gray level image. In order to enhance the security of image, the image is subsequently encrypted by the piecewise linear chaotic map in which the secret key of image encryption is determined by the initial of chaotic map. This stage of image encryption possesses high key and plain-image sensitivities which results from the secret key related to plain-image. Finally, the encrypted image is coded by the piecewise linear chaotic map with a different initial value. The experimental results validate the effect of the proposed system and demonstrate that the encrypted and coded image is secure for transmission.
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Avrutin, Viktor, Michael Schanz, and Björn Schenke. "Breaking the continuity of a piecewise linear map." ESAIM: Proceedings 36 (April 2012): 73–105. http://dx.doi.org/10.1051/proc/201236008.

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Weimou, Zheng. "Symbolic Dynamics of the Piecewise Linear Standard Map." Communications in Theoretical Physics 29, no. 3 (April 30, 1998): 369–76. http://dx.doi.org/10.1088/0253-6102/29/3/369.

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Just, Wolfram. "Analytical Approach for Piecewise Linear Coupled Map Lattices." Journal of Statistical Physics 90, no. 3-4 (February 1998): 727–48. http://dx.doi.org/10.1023/a:1023272819435.

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Dissertations / Theses on the topic "Piecewise linear map"

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Commendatore, Pasquale, Ingrid Kubin, and Iryna Sushko. "Emerging Trade Patterns in a 3-Region Linear NEG Model: Three Examples." Springer, 2017. http://dx.doi.org/10.1007/978-3-319-65627-4_3.

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This chapter draws attention to a specific feature of a NEG model that uses linear (and not iso-elastic) demand functions, namely its ability to account for zero trade. Thus, it represents a suitable framework to study how changes in parameters that are typical for NEG models, such as trade costs and regional market size, not only shape the regional distribution of economic activity, but at the same time determine the emergence of additional trade links between formerly autarkic regions. We survey some related papers and present a three-region framework that potentially nests many possible trade patterns. To focus the analysis, we study in more detail three specific trade patterns frequently found in the EU trade network. We start with three autarkic regions; then we introduce the possibility that two regions trade with each other; and, finally, we allow for one region trading with the other two, but the latter are still not trading with each other. We find a surprising plethora of long-run equilibria each involving a specific regional distribution of economic activity and a specific pattern of trade links. We show how a reduction in trade costs shapes simultaneously industry location and the configuration of the trade network.
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Lima, Amanda de. "Transversal families of piecewise expanding maps." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-01092015-215746/.

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Let t:[a,b] → ft be a C2 family of \"good\" C4 e piecewise expanding unimodal maps, with a critical point c, that is transversal to the topological classes of such maps. Given a lipchitzian observable ∅, consider the function ℛ∅(t)=∫∅dµt, where µt is the unique bsolutely continuous invariant probability of ft. We show a central limit theorem for the modulus of continuity of ℝ∅, that is limh→0m{t ∈ [a,b] : t + h ∈ [a,b] e 1/(Ψ(t)(-log|h|)½)((ℛ∅(t + h) - ℛ∅(t))/h) ≤ y} converges to 1/(2π)½ ∫y-∞e-s2/2ds. Now, let us consider a C2+ε expanding map f : 𝕊1 → 𝕊1 and a C1+ε periodic function v : 𝕊1 → ℝ. We show that the unique bounded solution of the twisted cohomological equation v(x) = α(f(x)) - Df(x)α(x) is either of class C1+ε or nowhere differentiable. We also prove that if α is nowhere differentiable, them the modulus of continuity of α satisfies a central limit theorem, that is, there is α > 0 such that limh→0µ{x : (α(x + h) - α(x))/(σ𝓁h(-log|h|)½) ≤ y} = 1/(2π)½ ∫y-∞e-t2/2dt, where µ is the absolutely continuous invariant probability of f.
Seja t:[a,b] → ft uma família C2 \"boa\" de transformações unimodais expansoras por pedaços com um ponto crítico c, que é transversal às classes topológicas de tais transformações. Dado um observável lipschitziano ∅, considere a função ℛ∅(t)=∫∅dµt, onde µt é a única probabiidade invariante absolutamente contínua de ft. Mostramos um teorema do limite central para o módulo de continuidade de ℝ∅, isto é limh→0m{t ∈ [a,b] : t + h ∈ [a,b] e 1/(Ψ(t)(-log|h|)½)((ℛ∅(t + h) - ℛ∅(t))/h) ≤ y} converge para 1/(2π)½ ∫y-∞e-s2/2ds. Vamos considerar agora f : 𝕊1 → 𝕊1 uma transformação expansora de classe C2+ε e v : 𝕊1 → ℝ uma função periódica de classe C1+ε. Mostramos que a única solução limitada da equação cohomológica torcida v(x) = α(f(x)) - Df(x)α(x) ou é de classe C1+ε ou não possui derivada em ponto algum. Mostramos também que se α não possui derivada em ponto algum, então o módulo de continuidade de α satisfaz um teorema do limite central, isto é, existe α > 0 tal que limh→0µ{x : (α(x + h) - α(x))/(σ𝓁h(-log|h|)½) ≤ y} = 1/(2π)½ ∫y-∞e-t2/2dt, onde µ é a probabilidade invariante absolutamente contínua associada a f.
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Feltekh, Kais. "Analyse spectrale des signaux chaotiques." Phd thesis, INSA de Toulouse, 2014. http://tel.archives-ouvertes.fr/tel-01071919.

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Au cours des deux dernières décennies, les signaux chaotiques ont été de plus en plus pris en compte dans les télécommunications, traitement du signal ou transmissions sécurisées. De nombreux articles ont été publiés qui étudient la densité spectrale de puissance (DSP) des signaux générés par des transformations spécifiques. La concentration sur la DSP est due à l'importance de la fréquence dans les télécommunications et la transmission sécurisée. Grâce au grand nombre de systèmes sans fil, la disponibilité des fréquences de transmission et de réception est de plus en plus rare pour les communications sans fil. Aussi, les médias guidés ont des limitations liées à la bande passante du signal. Dans cette thèse, nous étudions certaines propriétés associées à la bifurcation collision de frontière pour une transformation unidimensionnelle linéaire par morceaux avec trois pentes et deux paramètres. Nous calculons les expressions analytiques de l'autocorrélation et de la densité spectrale de puissance des signaux chaotiques générés par les transformations linéaires par morceaux. Nous montrons l'existence d'une forte relation entre les différents types de densité spectrale de puissance (passe-bas, passe-haut ou coupe-bande) et les paramètres de bifurcation. Nous notons également en évidence une relation entre le type de spectre et l'ordre des cycles attractifs. Le type du spectre dépend de l'existence des orbites périodiques au-delà de la bifurcation de collision de frontière qui a donné naissance au chaos. Nous utilisons ensuite les transformations chaotiques pour étudier la fonction d'ambiguïté. Nous combinons quelques transformations chaotiques bien déterminées pour obtenir un spectre large bande avec une bonne fonction d'ambiguïté qui peut être utilisée en système radar.
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Bondarenko, Ievgen. "Groups generated by bounded automata and their schreier graphs." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-2081.

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Marques, João Francisco Magro. "Dynamics of financial markets : study of an agent-based model." Master's thesis, Instituto Superior de Economia e Gestão, 2015. http://hdl.handle.net/10400.5/9328.

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Mestrado em Matemática Financeira
Nas últimas décadas, o mercado financeiro mundial tem enfrentado vários problemas e colapsos que motivaram anos conturbados para a economia real e para as famílias. Os sistemas dinâmicos apareceram na literatura de matemática financeira para ajudar a compreender melhor as características únicas destes mercados financeiros e a dinâmica do preço ao longo do tempo. Este trabalho consiste principalmente numa aproximação estatística ao sistema dinâmico de modelo de mercado com um ponto de descontinuidade introduzido por Tramontana, Westerhoff e Gardini (2010). Usando uma versão do modelo que produz órbitas caóticas, podemos observar, para parâmetros específicos, distribuições estacionárias. Por outras palavras, o sistema dinâmico pode ser caótico do ponto de vista do estudo das órbitas, porém, em termos estatísticos, é assintoticamente previsível, isto é, a maioria das trajetórias converge para um atractor que nós conseguimos descrevê-lo estatisticamente. Ainda, para os parâmetros apropriados, o modelo pode projetar um comportamento absolutamente errático, mesmo numa aproximação estatística. Para este último, nós concluímos que a previsão do preço é impossível uma vez que só conseguimos restringir os nossos prognósticos a um intervalo invariante suficientemente grande que contém toda a dinâmica do preço.
Over the past few decades, the global financial market has been facing multiple distresses and crashes which led to troubled years for the real economy and families. Dynamical systems emerged in the mathematical finance literature to help comprehending better the unique characteristics of these financial markets and the price dynamics over the time. This work consists mainly of a statistical approach of the one discontinuity point dynamical system market model introduced by Tramontana, Westerhoff and Gardini (2010). Using a model's version that produces chaotic orbits, we can observe stationary distributions under specific parameters. In other words, the dynamical system can be chaotic in a point-wise perspective, however, from a statistical approach, it can be asymptotically predictable, that is, most trajectories converge to an attractor which we can describe statistically. Still, under the proper parameters, the model may project an absolute erratic behavior, even in the statistical approach sense. For the latter, we conclude the price forecast is impossible because we can only restrict our prognoses to an invariant set sufficient large whose contain the whole price dynamic.
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SILVA, Thársis Souza. "Equações Diferenciais por partes:ciclos limite e cones invaiantes." Universidade Federal de Goiás, 2011. http://repositorio.bc.ufg.br/tede/handle/tde/1945.

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Made available in DSpace on 2014-07-29T16:02:18Z (GMT). No. of bitstreams: 1 Dissertacao Tharsis Souza Silva.pdf: 1389814 bytes, checksum: c28dfe55ac776a4de30d43875907dc64 (MD5) Previous issue date: 2011-03-25
In this work, we consider classes of discontinuous piecewise linear systems in the plane and continuous in the space. In the plane, we analyze systems of focus-focus (FF), focusparabolic (FP) and parabolic-parabolic (PP) type, separated by the straight line x = 0, and we prove that can appear until two limit cycles depending of parameters variations. Also we study a specific system, piecewise, with two saddles (one fixed in the origin and the other in the neighborhood of point (1;1)) separated by the straight line y= -x+1, and we show that can appear until two limit cycles depending of parameters variations. Finally, we examine a continuous piecewise linear system in R³ and we prove the existence of invariant cones and, through this structures, we determine some stable and unstable behavior.
Neste trabalho, consideramos classes de sistemas lineares por partes descontínuos no plano e contínuos no espaço. No plano, analisamos sistemas do tipo foco-foco (FF), parabólico-foco (PF) e parabólico-parabólico (PP) separados pela reta x = 0 e demonstramos que podem aparecer até dois ciclos limite, dependendo de variações de parâmetros. Também estudamos um sistema específico, linear por partes, com duas selas (uma sela fixa na origem e outra na vizinhança do ponto (1;1)) separadas pela reta y= -x+1 , e mostramos que podem aparecer até dois ciclos limite dependendo de variações de parâmetros. Por fim, examinamos um sistema linear por partes contínuo em R³ e demonstramos a existência de cones invariantes e, através destas estruturas, determinamos alguns comportamentos estáveis e instáveis.
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Books on the topic "Piecewise linear map"

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Levitt, N. Grassmannians and Gauss maps in piecewise-linear and piecewise-differentiable topology. Berlin: Springer-Verlag, 1989.

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Levitt, Norman. Grassmannians and Gauss Maps in Piecewise-linear Topology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0084994.

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Spaces of PL Manifolds and Categories of Simple Maps. Princeton University Press, 2013.

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Book chapters on the topic "Piecewise linear map"

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Mira, Christian. "Embedding of a Dim1 Piecewise Continuous and Linear Leonov Map into a Dim2 Invertible Map." In Global Analysis of Dynamic Models in Economics and Finance, 337–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29503-4_13.

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Aguirre, Carlos, Doris Campos, Pedro Pascual, and Eduardo Serrano. "A Model of Spiking-Bursting Neuronal Behavior Using a Piecewise Linear Two-Dimensional Map." In Computational Intelligence and Bioinspired Systems, 130–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11494669_17.

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Zhang, Xueping, Yawei Liu, Jiayao Wang, and Haohua Du. "A Novel Spatial Obstructed Distance by Dynamic Piecewise Linear Chaotic Map and Dynamic Nonlinear PSO." In Lecture Notes in Computer Science, 468–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13498-2_61.

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Aguirre, Carlos, Doris Campos, Pedro Pascual, and Eduardo Serrano. "Neuronal Behavior with Sub-threshold Oscillations and Spiking/Bursting Activity Using a Piecewise Linear Two-Dimensional Map." In Artificial Neural Networks: Biological Inspirations – ICANN 2005, 103–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11550822_17.

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Pumariño, A., J. A. Rodríguez, J. C. Tatjer, and E. Vigil. "Piecewise Linear Bidimensional Maps as Models of Return Maps for 3D Diffeomorphisms." In Progress and Challenges in Dynamical Systems, 351–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38830-9_22.

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Tramontana, Fabio, and Frank Westerhoff. "One-Dimensional Discontinuous Piecewise-Linear Maps and the Dynamics of Financial Markets." In Global Analysis of Dynamic Models in Economics and Finance, 205–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29503-4_9.

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Ding, Yiming, Hui Hu, and Yueli Yu. "On Hausdorff Dimension of Invariant Sets for a Class of Piecewise Linear Maps." In Difference Equations, Discrete Dynamical Systems and Applications, 67–82. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24747-2_5.

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Geronimo, J. S., and D. P. Hardin. "An Exact Formula for the Measure Dimensions Associated with a Class of Piecewise Linear Maps." In Constructive Approximation, 89–98. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-6886-9_5.

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Li, Shujun, Qi Li, Wenmin Li, Xuanqin Mou, and Yuanlong Cai. "Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding." In Cryptography and Coding, 205–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45325-3_19.

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Waldhausen, Friedhelm, Bjørn Jahren, and John Rognes. "The stable parametrized h-cobordism theorem." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186). Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691157757.003.0002.

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This chapter deals with the stable parametrized h-cobordism theorem. It begins with a discussion of the manifold part; here DIFF is written for the category of Csuperscript infinity smooth manifolds, PL for the category of piecewise-linear manifolds, and TOP for the category of topological manifolds. CAT is generically written for any one of these geometric categories. Relevant terms such as stabilization map, simple map, pullback map, PL Serre fibrations, weak homotopy equivalence, PL Whitehead space, and cofibration are also defined. The chapter proceeds by describing the non-manifold part, the algebraic K-theory of spaces, and the relevance of simple maps to the study of PL homeomorphisms of manifolds.
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Conference papers on the topic "Piecewise linear map"

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Metri, Rajanikant A., Mallareddy Mounica, and Bhooshan A. Rajpathak. "Characterization of 1D Linear Piecewise-Smooth Discontinuous Map." In 2020 IEEE First International Conference on Smart Technologies for Power, Energy and Control (STPEC). IEEE, 2020. http://dx.doi.org/10.1109/stpec49749.2020.9297744.

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Zhong, Yan-Ru, Hua-Yi Liu, Xi-Yan Sun, Ru-Shi Lan, and Xiao-Nan Luo. "Image Encryption Using 2D Sine-Piecewise Linear Chaotic Map." In 2018 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR). IEEE, 2018. http://dx.doi.org/10.1109/icwapr.2018.8521240.

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Holm, Peter D., Börje Nilsson, Louis Fishman, Anders Karlsson, and Sven Nordebo. "Wide-Angle Shift-Map PE for a Piecewise Linear Terrain." In MATHEMATICAL MODELING OF WAVE PHENOMENA: 3rd Conference on Mathematical Modeling of Wave Phenomena, 20th Nordic Conference on Radio Science and Communications. AIP, 2009. http://dx.doi.org/10.1063/1.3117113.

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Ivanov, Yu Yu, A. N. Romanyuk, A. Ia Kulyk, and O. V. Stukach. "A novel suboptimal piecewise-linear-log-MAP algorithm for turbo decoding." In 2015 International Siberian Conference on Control and Communications (SIBCON). IEEE, 2015. http://dx.doi.org/10.1109/sibcon.2015.7147195.

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wang, Yun-feng, Man-de Xie, and Ai-Ming Ji. "Research on a Piecewise Linear Chaotic Map and Its Cryptographical Application." In Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007). IEEE, 2007. http://dx.doi.org/10.1109/fskd.2007.470.

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Addabbo, Tommaso, Massimo Alioto, Ada Fort, Santina Rocchi, and Valerio Vignoli. "Maximum-Period PRNGs Derived From A Piecewise Linear One-Dimensional Map." In 2007 IEEE International Symposium on Circuits and Systems. IEEE, 2007. http://dx.doi.org/10.1109/iscas.2007.377903.

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Wasi, Muhammad Arif Ali, and Susila Windarta. "Modified SNOW 3G: Stream cipher algorithm using piecewise linear chaotic map." In PROCEEDINGS OF THE 7TH SEAMS UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2015: Enhancing the Role of Mathematics in Interdisciplinary Research. AIP Publishing LLC, 2016. http://dx.doi.org/10.1063/1.4940850.

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Peng, Jun, Shangzhu Jin, Yongguo Liu, Zhiming Yang, Mingying You, and Yangjun Pei. "A novel scheme for image encryption based on piecewise linear chaotic map." In 2008 IEEE Conference on Cybernetics and Intelligent Systems (CIS). IEEE, 2008. http://dx.doi.org/10.1109/iccis.2008.4670966.

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Yoshioka, Daisaburo. "Hardware implementable S-box based on a discretized piecewise linear chaotic map." In 2013 9th International Wireless Communications and Mobile Computing Conference (IWCMC 2013). IEEE, 2013. http://dx.doi.org/10.1109/iwcmc.2013.6583714.

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Rhouma, Rhouma, David Arroyo, and Safya Belghith. "A new color image cryptosystem based on a piecewise linear chaotic map." In 2009 6th International Multi-Conference on Systems, Signals and Devices (SSD). IEEE, 2009. http://dx.doi.org/10.1109/ssd.2009.4956666.

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