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Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

Łukasz Korus (2014)

International Journal of Applied Mathematics and Computer Science

The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms...

Egorov theorems and equidistribution of eigenfunctions for the quantized sawtooth and Baker maps

S. De Bièvre, M. Degli Esposti (1998)

Annales de l'I.H.P. Physique théorique

Eigenmodes of the damped wave equation and small hyperbolic subsets

Gabriel Rivière (2014)

Annales de l’institut Fourier

We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of $β$ -damped stationary solutions cannot be completely concentrated in small neighborhoods of a small fixed hyperbolic subset made of $β$ -damped trajectories of the geodesic flow.The article also includes an appendix (by S. Nonnenmacher and the author) where we establish the existence of an inverse logarithmic strip without eigenvalues...

EKF-based dual synchronization of chaotic colpitts circuit and Chua’s circuit

Shaohua Hong, Zhiguo Shi, Kangsheng Chen (2008)

Kybernetika

In this paper, dual synchronization of a hybrid system containing a chaotic Colpitts circuit and a Chua’s circuit, connected by an additive white Gaussian noise (AWGN) channel, is studied via numeric simulations. The extended Kalman filter (EKF) is employed as the response system to achieve the dual synchronization. Two methods are proposed and investigated. The first method treats the combination of a Colpitts circuit and a Chua’s circuit as a higher- dimensional system, while the second method...

Embedding inverse limits interval maps as attractors

Michał Misiurewicz (1985)

Fundamenta Mathematicae

Embedding tiling spaces in surfaces

Charles Holton, Brian F. Martensen (2008)

Fundamenta Mathematicae

We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms...

Entropies des flots magnétiques

Stéphane Grognet (1999)

Annales de l'I.H.P. Physique théorique

Entropy and localization of eigenfunctions

Nalini Anantharaman (2006/2007)

Séminaire Équations aux dérivées partielles

Entropy linearity and chain-recurrence

David Fried, Michael Shub (1979)

Publications Mathématiques de l'IHÉS

Entropy of eigenfunctions of the Laplacian in dimension 2

Gabriel Rivière (2010)

Journées Équations aux dérivées partielles

We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [4] by proving that the Kolmogorov-Sinai entropy of a semiclassical measure $μ$ for the geodesic flow $g^{t}$ is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the $37^{èmes}$ Journées EDP (Port d’Albret-June, 7-11 2010))

Entropy of Geodesic Flow and Exponent of Convergence of Some Dirichlet Series.

Su-shing Chen (1981)

Mathematische Annalen

Entropy-expansiveness and domination for surface diffeomorphisms.

María José Pacifico, José L. Vieitez (2008)

Revista Matemática Complutense

Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions

Maíra Aguiar, Bob Kooi, Nico Stollenwerk (2008)

Mathematical Modelling of Natural Phenomena

Basic models suitable to explain the epidemiology of dengue fever have previously shown the possibility of deterministically chaotic attractors, which might explain the observed fluctuations found in empiric outbreak data. However, the region of bifurcations and chaos require strong enhanced infectivity on secondary infection, motivated by experimental findings of antibody-dependent-enhancement. Including temporary cross-immunity in such models, which is common knowledge among field researchers...

Equilibrium measures for holomorphic endomorphisms of complex projective spaces

Mariusz Urbański, Anna Zdunik (2013)

Fundamenta Mathematicae

Let f: ℙ → ℙ be a holomorphic endomorphism of a complex projective space $ℙ^{k}$ , k ≥ 1, and let J be the Julia set of f (the topological support of the unique maximal entropy measure). Then there exists a positive number $κ_{f} > 0$ such that if ϕ: J → ℝ is a Hölder continuous function with $s u p (ϕ) - i n f (ϕ) < κ_{f}$ , then ϕ admits a unique equilibrium state $μ_{ϕ}$ on J. This equilibrium state is equivalent to a fixed point of the normalized dual Perron-Frobenius operator. In addition, the dynamical system $(f, μ_{ϕ})$ is K-mixing, whence ergodic. Proving...

Equilibrium states for interval maps: the potential $- t log | D f |$

Henk Bruin, Mike Todd (2009)

Annales scientifiques de l'École Normale Supérieure

Let $f : I \to I$ be a $C^{2}$ multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential $φ_{t} : x \mapsto - t log | D f (x) |$ for $t$ close to $1$ , and also that the pressure function $t \mapsto P (φ_{t})$ is analytic on an appropriate interval near $t = 1$ .

Equivalence between subshrubs and chaotic bands in the Mandelbrot set.

Pastor, G., Romera, M., Alvarez, G., Arroyo, D., Montoya, F. (2006)

Discrete Dynamics in Nature and Society

Ergodic geodesic flows on product manifolds with low dimensional factors.

Keith Burns, Marlies Gerber (1994)

Journal für die reine und angewandte Mathematik

Ergodic properties and KMS conditions on $C^{*}$ -symbolic dynamical systems.

Matsumoto, Kengo (2011)

Documenta Mathematica

Ergodic theory approach to chaos: Remarks and computational aspects

Paweł J. Mitkowski, Wojciech Mitkowski (2012)

International Journal of Applied Mathematics and Computer Science

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a...

Ergodic theory of interval exchange maps.

Marcelo Viana (2006)

Revista Matemática Complutense

A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators, and Teichmüller flows, starting from the basic definitions and culminating with the proof that almost every interval exchange map is uniquely ergodic. Great emphasis is put on examples and geometric interpretations of the main ideas.

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