Related papers: Similarity Between Two Dynamical Systems
In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…
The dynamics of the one-tangle and the concurrence is analyzed in the Lipkin-Meshkov-Glick model which describes many physical systems such as the two-mode Bose-Einstein condensates. We consider two different initial states which are…
To each dynamic equivalence of two control systems is associated an infinite permutation matrix. We investigate how such matrices are related to the existence of dynamic equivalences.
Given a dynamical system $(X, \Gamma)$, the corresponding crossed product $C^*$-algebra $C(X)\rtimes_{r}\Gamma$ is called reflecting, when every intermediate $C^*$-algebra $C^*_r(\Gamma)<\mathcal{A} < C(X)\rtimes_{r}\Gamma$ is of the form…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
Takens' Embedding Theorem asserts that when the states of a hidden dynamical system are confined to a low-dimensional attractor, complete information about the states can be preserved in the observed time-series output through the delay…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
Dynamical System has been widely used for encoding trajectories from human demonstration, which has the inherent adaptability to dynamically changing environments and robustness to perturbations. In this paper we propose a framework to…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
This paper considers a problem of testing, from a finite sample, a topological conjugacy of two dynamical systems $(X,f)$ and $(Y,g)$. More precisely, given $x_1,\ldots, x_n \subset X$ and $y_1,\ldots,y_n \subset Y$ such that $x_{i+1} =…
Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…
A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…
We study an algebraic analog of a C*-algebra associated to a generalized Boolean dynamical system which parallels the relation between graph C*-algebras and Leavitt path algebras. We prove that such algebras are Cuntz-Pimsner algebras and…
Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of nonlinear dynamic behavior (e.g. through normal forms). In…
We consider the reduced dynamics in a bipartite quantum system (consisting of a central system and an intermediate environment) coupled to a heat bath at finite temperature. To describe this situation, in the simplest possible -- yet…
We use the structure theory of minimal dynamical systems to show that, for a general group $\Gamma$, a tame, metric, minimal dynamical system $(X, \Gamma)$ has the following structure: \begin{equation*} \xymatrix {& \tilde{X} \ar[dd]_\pi…
The conformance testing problem for dynamical systems asks, given two dynamical models (e.g., as Simulink diagrams), whether their behaviors are "close" to each other. In the semi-formal approach to conformance testing, the two systems are…
We study the dynamical regimes that emerge from the strongly coupling between two Chua's circuits with parameters mismatch. For the region around the perfect synchronous state we show how to combine parameter diversity and coupling in order…