Related papers: Multifractal analysis of nonhyperbolic coupled map…
The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long range…
Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each…
Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we…
Coupled map lattices are a paradigm of higher-dimensional dynamical systems exhibiting spatio-temporal chaos. A special case of non-hyperbolic maps are one-dimensional map lattices of coupled Chebyshev maps with periodic boundary…
We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess…
Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…
The scaling hypothesis for the coupled chotic map lattices (CML) is formulated. Scaling properties of the CML in the regime of extensive chaos observed numerically before is justified analytically. The asymptotic Liapunov exponents spectrum…
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for…
The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework…
Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, may have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic…
Motivation: With the advent of Language Models using Transformers, popularized by ChatGPT, there is a renewed interest in exploring encoding procedures that numerically represent symbolic sequences at multiple scales and embedding…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
Applying chaos theory for secure digital communications is promising and it is well acknowledged that in such applications the underlying chaotic systems should be carefully chosen. However, the requirements imposed on the chaotic systems…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of…
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical…
A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where…
In this work, we applied the Chaos Game Representation (CGR) to the complete human genomic sequence T2T-CHM13v2.0, analyzing the entire chromosome assembly and each chromosome separately, including mitochondrial DNA. Multifractal spectra…
Modern biological techniques such as Hi-C permit to measure probabilities that different chromosomal regions are close in space. These probabilities can be visualised as matrices called contact maps. In this paper, we introduce a…
The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and…