Related papers: Multishadowing in topological dynamics
We propose an information-based model for network dynamics in which imperfect information leads to networks where the different vertices have widely different number of edges to other vertices, and where the topology has hierarchical…
In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two…
Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics -- a grand-challenge open problem. Here, we show…
In this paper, controllability of undirected networked systems with {diffusively coupled subsystems} is considered, where each subsystem is of {identically {\emph{fixed}}} general high-order single-input-multi-output dynamics. The…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
We develop a new metric and inverse-limit framework for Deaconu-Renault systems arising from local homeomorphisms between open subsets of locally compact zero-dimensional spaces. Our starting point is the Paterson-type compactification of…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…
The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…
Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments…
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…
In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
The phenomenon of shadowing of nuclear structure functions at small values of Bjorken-$x$ is analyzed. First, multiple scattering is discussed as the underlying physical mechanism. In this context three different but related approaches are…
We consider inverse periodic shadowing properties of discrete dynamical systems generated by diffeomorphisms of closed smooth manifolds. We show that the $C^1$-interior of the set of all diffeomorphisms having so-called inverse periodic…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…