Related papers: Similarity Between Two Dynamical Systems
We introduce dynamical systems $(X,G)$ with closed relations $G$ on compact metric spaces $X$ and discuss different types of minimality of such dynamical systems, all of them generalizing minimal dynamical systems $(X,f)$ with continuous…
In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…
The Koopman linearization of measure-preserving systems or topological dynamical systems on compact spaces has proven to be extremely useful. In this article we look at dynamics given by continuous semiflows on completely regular spaces…
A simple model to investigate the long time dynamics of glass-formers is presented and applied to study a Lennard-Jones system in supercooled and glassy phases. According to our model, the point representing the system in the…
Chen, Faudree, Gould, Jacobson, and Lesniak determined the minimum degree threshold for which a balanced $k$-partite graph has a Hamiltonian cycle. We give an asymptotically tight minimum degree condition for Hamiltonian cycles in arbitrary…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
Given a linear dynamical system, we consider the problem of constructing an approximate system using only a subset of the sensors out of the total set such that the observability Gramian of the new system is approximately equal to that of…
Partial integrability in phase-oscillator dynamics is typically examined for identically connected oscillators or groups thereof. Yet, the precise connectivity conditions that ensure conserved quantities on general networks remain unclear.…
We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated…
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…
We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of…
This paper presents a novel approach to analyze quasiperiodically driven dynamical systems. It aims to develop a complete data-driven framework for modeling such unknown dynamics. To achieve this, we characterize Koopman eigenfrequencies as…
We analyse the entanglement dynamics of the two particles interacting through gravity in the recently proposed experiments aiming at testing quantum signatures for gravity [Phy. Rev. Lett 119, 240401 & 240402 (2017)]. We consider the open…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
We consider the dynamics and stationary regime of a capacitively-shunted transmon-type qubit in front of a mirror, affected by two signals: probe and dressing signals. By varying the parameters of these signals and then analyzing the probe…
This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma_1 \subset \Gamma_2 \subset \Re^n$, with…
In Mathematical Morphology (MM), connected filters based on dynamics are used to filter the extrema of an image. Similarly, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) that represents the stability of…
In network science, collective dynamics of complex systems are typically modelled as (nonlinear, often including many-body) vertex-level update rules evolving over a graph interaction structure. In recent years, frameworks that explicitly…
Study of the nonlinear evolution deep neural network (DNN) parameters undergo during training has uncovered regimes of distinct dynamical behavior. While a detailed understanding of these phenomena has the potential to advance improvements…
We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of…