Related papers: Some Variations of Transitivity for CR-dynamical s…
Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger…
Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to anyarbitrary region, and the fluxes between any two regions. The considered description offers a general and unified…
Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…
Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of $\Cal B(H)$ endowed with a certain causal structure. With any interaction there is a well-defined…
Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the…
Continuous Time Random Walks (CTRW) are widely used to coarse-grain the evolution of systems jumping from a metastable sub-set of their configuration space, or trap, to another via rare intermittent events. The multi-scaled behavior typical…
For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…
Reformulating constitutive relation in terms of gradient dynamics (being derivative of a dissipation potential) brings additional information on stability, metastability and instability of the dynamics with respect to perturbations of the…
Temporal graphs represent interactions between entities over time. These interactions may be direct, a contact between two vertices at some time instant, or indirect, through sequences of contacts called journeys. Deciding whether an entity…
An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…
We focus in this work on the study of traffic in open systems using a modified version of an existing cellular automaton model. We demonstrate that the open system is rather different from the closed system in its 'choice' of a unique…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
This paper presents the basic concepts of a systemic theory of interaction between non-deterministic open dynamics with varying temporalities, which includes three stages: the definition of these dynamics as lax-functors, the notion of…
The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…
The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering…
We propose a measure for genuine multipartite correlations suited for the study of dynamics in open quantum systems. This measure is contextual in the sense that it depends on how information is read from the environment. It is used to…
This paper studies the controllability of networked relative coupling systems (NRCSs), in which subsystems are of fixed high-order linear dynamics and coupled through relative variables depending on their neighbors, from a structural…
We discuss topological equicontinuity and even continuity in dynamical systems. In doing so we provide a classification of topologically transitive dynamical systems in terms of equicontinuity pairs, give a generalisation of the…