Abstract Let A be a finite set and let ϕ: ℤ →ℝ locally constant potential. For each β >0 (‘inverse temperature’), there is unique Gibbs measure μ ϕ . We prove that as →+ ∞ , the family ( ) converges (in weak- * topology) to we characterize. This concentrated on certain subshift of type, which union transitive subshifts type. The two main tools are an approximation by periodic orbits Perron–Frobenius theorem for matrices à la Birkhoff. crucial idea bring ‘renormalization’ procedure...

Genetic regulatory networks are usually modelled by systems of coupled differential equations, and more particularly piecewise affine equations. Finite state models, better known as logical networks, also used. In this paper we present a class models which may be situated in the middle spectrum; they both discrete continuous aspects. They consist network units, whose states quantified real variable. The each unit evolves according to contractive transformation chosen from finite collection...

We are interested in the phenomenology of asymptotic dynamics piecewise contracting maps. consider a wide class such maps and we give sufficient conditions to ensure some general basic properties, as periodicity, total disconnectedness or zero Lebesgue measure attractor. These show particular that non-periodic attractor necessarily contains discontinuities map. Under this hypothesis, obtain numerous examples attractors, ranging from finite connected chaotic, contrasting with (quasi-)periodic...

Motivated by entropy estimation from chaotic time series, we pro-vide a comprehensive analysis of hitting times cylinder sets in the settingof Gibbsian sources. We prove two strong approximation results whichwe easily deduce pointwise convergence to entropy, lognormal fluctuations,precise large deviation estimates and an explicit formula for hitting-timemultifractal spectrum. It follows our that an-cylinder fluctuates same way as inverse measure this n-cylinderat 'small scales', but...

Abstract Let Σ be a finite alphabet, Ω=Σ ℤ d equipped with the shift action, and ℐ simplex of shift-invariant measures on Ω. We study relation between restriction n to cubes {− ,…, } ⊂ℤ , polytope ‘locally invariant’ loc . are especially interested in geometry convex set which turns out strikingly different when =1 ≥2 A major role is played by shifts type naturally identified faces uniquely ergodic type, whose unique invariant measure gives rise extreme points although dimension there also...

Cryptosystems for binary information are based on two primitives: an indexed family of permutations words and a generator pseudorandom sequences indices. A very efficient implementation the primitives is constructed using phenomenon synchronization in cellular automata. (c) 1998 American Institute Physics.

Starting from the full--shift on a finite alphabet $A$, mingling some symbols of we obtain new full shift smaller $B$. This amalgamation defines factor map $(A^{\mathbb N},T_A)$ to $(B^{\mathbb N},T_B)$, where $T_A$ and $T_B$ are respective maps. According thermodynamic formalism, each regular function (`potential') $ψ:A^{\mathbb N}\to{\mathbb R}$, can associate unique Gibbs measure $μ_ψ$. In this article, prove that, for large class potentials, pushforward $μ_ψ\circπ^{-1}$ is still Gibbsian...

The phenomenon of synchronization in pairs cellular automata coupled a driver-replica mode is studied. Necessary and sufficient conditions for linear automaton are given. couplings that make pair synchronize determined all elementary automata. (c) 1998 American Institute Physics.

The spectra of Poincaré recurrences for two classes dynamicalsystems are obtained in the framework Carathéodory construction. Oneclass contains systems which topologically conjugate to subshifts with thespecification property, other consists minimal multipermutative symbolic systems. shown be solutions a non-homogeneousBowen equation, and their relationship multifractal Lyapunovexponents is exposed.

We analyze urban spatial segregation phenomenon in terms of the income distribution over a population, and an inflationary parameter weighting evolution housing prices. For this, we develop discrete spatially extended model based on multiagent approach. In our model, mobility socioeconomic agents is driven only by Agents exchange location order to fit their status cost housing. On other hand, price particular house depends its tenant, neighborhood mean lodging weighted control parameter. The...

Consider a Hölder continuous potential ϕ defined on the full shift , where A is finite alphabet. Let be specified sofic subshift. It well known that there unique Gibbs measure μϕ X associated with ϕ. In addition, natural nested sequence of subshifts type (Xm) converging to subshift X. To this we can associate measures . paper, prove these converge weakly at exponential speed (in classical distance metrizing weak topology). We also establish mixing property implies Bernoulli. Finally,...

We study the direction dependence of density directional entropy in lattice dynamical systems. show that if dynamics is homogeneous and continuous, then this does not depend on space–time. By using symbolic we derive formulae for weakly coupled hyperbolic maps. As a corollary, present examples where actually depends direction, provided individual subsystems are sufficiently different.

We introduce a method for estimating the complexity function (which counts number of observable words given length) finite symbolic sequence, which we use to estimate coding DNA sequences several species Hominidae family. In all cases, obtained complexities show same characteristic behavior: exponential growth small word lengths, followed by linear larger lengths. The consider exhibit systematic trend in correspondence with phylogenetic tree. Using our method, some known evolution models,...

One of the fields applied mathematics is related to model analysis. Biomedical systems are suitable candidates for this field because their importance in life sciences including therapeutics. Here we deal with analysis a recently proposed by Espinoza-Valdez et al. (2010) kidney vasculature developed via angiogenesis. The graph theory allows one quantitatively vascular arterial tree sense that (1) vertex represents vessels bifurcation, whereas (2) each edge stands vessel physiological...

A new class of b-adic normal numbers is built recursively by using Eulerian paths in a sequence de Bruijn digraphs. In this recursion, path constructed as an extension the previous one, such way that block determined contains maximal number different subblocks consecutive lengths most compact arrangement. Any source redundancy avoided at every step. Our recursive construction alternative to several well-known concatenative constructions à la Champernowne.

We study the complexity of stable waves in unidirectional bistable coupled map lattices as a test tube to spatial chaos traveling patterns open flows. Numerical calculations reveal that, grouping into sets according their velocity, at most one set has positive topological entropy for fixed parameters. By using symbolic dynamics and shadowing, we analytically determine velocity-dependent parameter domains existence pattern families with entropy. These arguments provide method exhibit chaotic...