Related papers: The dependence on the initial states and the trans…
We identify general conditions under which regenerative processes with dependent cycles and cycle lengths are asymptotically independent. The result is applied to various models. In particular, independent L\'evy processes with dependent…
Let $\Phi:\{0,1\}^{n}\longrightarrow\{0,1\}^{n}$. The asynchronous flows are (discrete time and real time) functions that result by iterating the coordinates $\Phi_{i}$ independently on each other. The purpose of the paper is that of…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
Entry in: Encyclopedia of Algorithms, Ming-Yang Kao, Ed., Springer, To appear. Synonyms: Wait-free registers, wait-free shared variables, asynchronous communication hardware. Problem Definition: Consider a system of asynchronous processes…
The 'nice' $x:\mathbf{R}\rightarrow\{0,1\}^{n}$ functions from the asynchronous systems theory are called signals. The periodicity of a point of the orbit of the signal x is defined and we give a note on the existence of the prime period.
We consider two types of dynamical systems namely non-autonomous discrete dynamical systems(NDDS) and generic dynamical systems(GDS). In both of them, we study various notions of transitivity. We give many equivalent conditions for each of…
This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…
In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering. An asynchronous system f is a multi-valued function that assigns to each admissible input u a set f(u) of possible states x in…
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…
The paper is devoted to a mathematical model of concurrency the special case of which is asynchronous system. Distributed asynchronous automata are introduced here. It is proved that the Petri nets and transition systems with independence…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
For discrete autonomous dynamical systems (ADS) $(X, d, f)$, it was found that in the three conditions defining Devaney chaos, topological transitivity and dense periodic points together imply sensitive dependence on initial…