Related papers: Specification properties for non-autonomous discre…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
The widespread adoption of autonomous systems depends on providing guarantees of safety and functional correctness, at both design time and runtime. Information about the extent to which functional requirements can be met in combination…
In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is motivated by the desire to characterize local dynamical…
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
Motivated by the regulator theory and adaptive controls, several notions on output stability in the framework of input-to-state stability (iss) were introduced for finite-dimensional systems. It turned out that these output stability…
Non-statistical weak measurements yield weak values that are outside the range of eigenvalues and are not rare, suggesting that weak values are a property of every pre-and-post-selected ensemble. They also extend the applicability and valid…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
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…
In this paper, the interrelations of some dynamical properties of the non-autonomous dynamical system (X, f1;infinity) and its induced non-autonomous dynamical system (K(X), f1;infinity) are studied, where K(X) is the hyperspace of all…