Related papers: Average chain transitivity and the almost average …
The dual concepts of `universality' and `hypercyclicity' are better understood and studied as `topological transitivity'. In this article we consider transitivity properties of skew products, essentially with non-compact fibers. We study…
We consider a continuous-time quantum walk on a triple graph and investigate the influence of the side chain on the propagation in the main chain. Calculating the interchange of the probabilities between the two parts of the main chain, we…
Families of regimes for control systems are studied possessing the so called quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the degree of transients overshooting…
A numerical approach to the study of equilibrium statistical properties of spin-1/2 XY chains is suggested. The approach is illustrated by the examining of influence of disorder on transverse dynamical susceptibility of spin-1/2 Ising chain…
An important source of high clustering coefficient in real-world networks is transitivity. However, existing approaches for modeling transitivity suffer from at least one of the following problems: i) they produce graphs from a specific…
For any continuous self-map of a compact metric space, we prove a saturation of distributionally scrambled Mycielski sets under a type of shadowing and the chain transitivity.
An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
We study three notions of shadowing: classical shadowing, limit (or asymptotic) shadowing, and s-limit shadowing. We show that classical and s-limit shadowing coincide for tent maps and, more generally, for piecewise linear interval maps…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The paper presents a new numerical approach for studying the thermodynamical and dynamical properties of finite spin-$\frac{1}{2}$ $XY$ chains. Special attention is given to examining the influence of disorder on the average transverse…
Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the…
Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different "layers" that each represent one of many possible subsystems or types…
This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix…
We examine the ground state properties of the s=1/2 transverse Ising chain with regularly alternating bonds and fields using exact analytical results and exact numerical data for long (up to N=900) and short (N=20) chains. For a given…
This article is a discussion of some characteristic properties in connection with global models, particularly for the application of prediction, such as the approximation property, the interpolation property and the transmission property.
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to…
This review synthesizes recent advancements in understanding tipping points and cascading transitions within the Earth system, framing them through the lens of nonlinear dynamics and complexity science. It outlines the fundamental concepts…
We study properties of multi-layered, interconnected networks from an ensemble perspective, i.e. we analyze ensembles of multi-layer networks that share similar aggregate characteristics. Using a diffusive process that evolves on a…
We give a completely elementary study for averages of short correlations of so-called sieve functions (a pretty general class of arithmetic functions).