Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0707.0755

A cellular automaton identification of the universality classes of spatiotemporal intermittency

Zahera Jabeen·Neelima Gupte
View original source ↗Read source document ↗Export metadata ↓

Abstract

The phase diagram of the coupled sine circle map lattice shows spatio-temporal intermittency of two distinct types: spatio-temporal intermittency of the directed percolation (DP) class, and spatial intermittency which does not belong to this class. These two types of behaviour are seen to be special cases of the spreading and non-spreading regimes seen in the system. In the spreading regime, each site can infect its neighbours permitting an initial disturbance to spread, whereas in the non-spreading regime no infection is possible. The two regimes are separated by a line which we call the infection line. The coupled map lattice can be mapped on to an equivalent cellular automaton which shows a transition from a probabilistic cellular automaton (PCA) to a deterministic cellular automaton (DCA) at the infection line. Thus the existence of the DP and non-DP universality classes in the same system is signalled by the PCA to DCA transition. We also discuss the dynamic origin of this transition.

Explore related subjects

nlin.CD

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zahera Jabeen, Neelima Gupte. 2007-07-05. A cellular automaton identification of the universality classes of spatiotemporal intermittency. https://arxiv.org/abs/0707.0755

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Symmetry Transfer to Basins and Enhancement at Basin Boundaries

For an equivariant dynamical system, we prove that a compact Lyapunov-stable attractor realized as an $ω$-limit set has the same setwise symmetry group as its basin. Admissible attractor and basin symmetries therefore coincide within each fixed dynamical category. For a finite symmetry group, the index of the attractor stabilizer in the boundary stabilizer counts the symmetry-related basins sharing that full boundary. This yields a criterion for boundary symmetry enhancement, a dichotomy for attractor orbits of prime size, and a connection with Wada basins. A common boundary of $m$ disjoint open basins has at least $m$ local complementary components, which excludes smooth hypersurface patches when $m\geq 3$. Smooth flows and Newton maps illustrate the different possibilities.

nlin.CD↗
arXiv2026

Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics

We present an open-source Python package for sampling the Gaussian, Laguerre, Jacobi, and Circular $β$-ensembles of random matrix theory. The package implements the Dumitriu--Edelman and Killip--Nenciu constructions, allowing efficient generation of random spectra for general $β> 0$. In addition to spectrum generation, it includes tools for the analysis of spectral statistics, from standard nearest-neighbor spacings and spacing ratios to non-adjacent $k$-spacings and the spectral form factor. These tools can be applied to generic spectral data, allowing users to compare them with and fit them to $β$-ensemble predictions. In this note, we review the $β$-ensembles, describe the package interface, and illustrate its use through several numerical experiments motivated by applications to quantum chaos. Our numerical results include an analysis of $β$ as a continuous fitting parameter in spacing ratio statistics, an examination of the numerical evidence for the conjectured $k$-spacing ratio distributions, and a study of the spectral form factor for general values of $β$.

nlin.CD↗
arXiv2026

Attractors and basins generated by repeated sums of prime factors of natural numbers

Integer maps are discrete dynamical systems defined on the natural numbers. In this paper, we investigate the dynamics of the shifted Alladi-Erd{\H o}s map, a one-parameter family of integer maps in which each composite number is mapped to the sum of its prime factors, while each prime is mapped to $n+A$, where $A \in \mathbb{N}$ is a fixed shift parameter. By systematically exploring the parameter space for $2 \leq A \leq 10^5$, we uncover a rich bifurcation structure characterized by the emergence, disappearance, and reorganization of attractor cycles as the shift parameter varies. We find that although several attractors may coexist for a given value of $A$, for most values of $A$, almost all natural numbers belong to the basins of only two dominant attractors. Using elementary number theoretic arguments, we explain the observed bifurcation diagram. We further characterize the attractor cycles and quantify the distribution of their basin sizes across the parameter space. Our results reveal an unexpectedly rich landscape of arithmetic dynamics arising from a remarkably simple integer map. %and provide a systematic characterization of how attractors and their basins evolve as shift parameter is varied.

nlin.CD↗