Related papers: Multishadowing in topological dynamics
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let $X$…
Given a dynamical system $(X,f)$ we investigate several topological dynamical properties for its Zadeh extension $(\mathcal{F}(X),\hat{f})$ endowed with the endograph metric $d_{E}$. In particular, we prove that for some contractive and…
This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…
We investigate a shadowing property which appears naturally in the study of piecewise monotonic maps of the interval. It turns out to be a weak form of the rank one property, a well-known notion in abstract ergodic theory. We show that this…
We introduce a new dynamical system model called the shadowing problem, where a shadower chases after an escaper by always staring at and keeping the distance from him. When the escaper runs along a planar closed curve, we associate to the…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
We consider extensions of the notion of topological transitivity for a dynamical system $(X,f)$. In addition to chain transitivity, we define strong chain transitivity and vague transitivity. Associated with each there is a notion of…
We study the relation between the shadowing property and the limit shadowing property. We prove that if a continuous self-map $f$ of a compact metric space has the limit shadowing property, then the restriction of $f$ to the non-wandering…
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…
We consider a linear skew product with the full shift in the base and nonzero Lyapunov exponent in the fiber. We provide a sharp estimate for the precision of shadowing for a typical pseudotrajectory of finite length. This result indicates…
Accurate representation of the physical layer is required for analysis and simulation of multi-hop networking in sensor, ad hoc, and mesh networks. This paper investigates, models, and analyzes the correlations that exist in shadow fading…
A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different…
We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
When dealing with spreading processes on networks it can be of the utmost importance to test the reliability of data and identify potential unobserved spreading paths. In this paper we address these problems and propose methods for hidden…
A shadowable point for a flow is a point where the shadowing lemma holds for pseudo-orbits passing through it. We prove that this concept satisfies the following properties: the set of shadowable points is invariant and a $G_{\delta}$ set.…