Related papers: Measurable Time-Restricted Sensitivity
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
To link the Auslander point dynamics property with topological transitivity, in this paper we introduce dynamically compact systems as a new concept of a chaotic dynamical system $(X,T)$ given by a compact metric space $X$ and a continuous…
The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
Several studies demonstrate that there are critical differences between real wireless networks and simulation models. This finding has permitted to extract spatial and temporal properties for links and to provide efficient methods as biased…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
This paper is the first part of a project devoted to studying the interconnection between controllability properties of a dynamical system and the large-time asymptotics of trajectories for the associated stochastic system. It is proved…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
Time reversal of vast classes of phenomena has direct implications with predictability, causality and the second principle of thermodynamics. We analyze in detail time reversibility of a paradigmatic dissipative nonlinear dynamical system,…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the…
The notion of Li-Yorke sensitivity has been studied extensively in the case of topological dynamical systems. We introduce a measurable version of Li-Yorke sensitivity, for nonsingular (and measure-preserving) dynamical systems, and compare…