Página 1 dos resultados de 29229 itens digitais encontrados em 0.036 segundos

Dynamic Logics of Dynamical Systems

Platzer, André
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/05/2012 Português
Relevância na Pesquisa
67.224854%
We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of parametrized modal operators for each dynamical system to express necessary or possible properties of their transition behavior. Due to their full basis of first-order modal logic operators, dynamic logics can express a rich variety of system properties, including safety, controllability, reactivity, liveness, and quantified parametrized properties, even about relations between multiple dynamical systems. In this survey, we focus on some of the representatives of the family of differential dynamic logics, which share the ability to express properties of dynamical systems having continuous dynamics described by various forms of differential equations. We explain the dynamical system models, dynamic logics of dynamical systems, their semantics, their axiomatizations, and proof calculi for proving logical formulas about these dynamical systems. We study differential invariants, i.e., induction principles for differential equations. We survey theoretical results, including soundness and completeness and deductive power. Differential dynamic logics have been implemented in automatic and interactive theorem provers and have been used successfully to verify safety-critical applications in automotive...

Toric dynamical systems

Craciun, Gheorghe; Dickenstein, Alicia; Shiu, Anne; Sturmfels, Bernd
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
67.08657%
Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems and all detailed balancing systems. One feature is that the steady state locus of a toric dynamical system is a toric variety, which has a unique point within each invariant polyhedron. We develop the basic theory of toric dynamical systems in the context of computational algebraic geometry and show that the associated moduli space is also a toric variety. It is conjectured that the complex balancing state is a global attractor. We prove this for detailed balancing systems whose invariant polyhedron is two-dimensional and bounded.; Comment: We include the proof of our Conjecture 5 (now Lemma 5) and add some references

Non uniformly hyperbolic dynamics: H\'enon maps and related dynamical systems

Benedicks, Michael
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/04/2003 Português
Relevância na Pesquisa
67.122246%
In the 1960s and 1970s a large part of the theory of dynamical systems concerned the case of uniformly hyperbolic or Axiom A dynamical system and abstract ergodic theory of smooth dynamical systems. However since around 1980 an emphasize has been on concrete examples of one-dimensional dynamical systems with abundance of chaotic behavior (Collet &Eckmann and Jakobson). New proofs of Jakobson's one-dimensional results were given by Benedicks and Carleson \cite{BC85} and were considerably extended to apply to the case of H\'enon maps by the same authors \cite{BC91}. Since then there has been a considerable development of these techniques and the methods have been extended to the ergodic theory and also to other dynamical systems (work by Viana, Young, Benedicks and many others). In the cases when it applies one can now say that this theory is now almost as complete as the Axiom A theory.

Modular dynamical systems on networks

DeVille, Lee; Lerman, Eugene
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/03/2013 Português
Relevância na Pesquisa
67.1582%
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations, on the other hand, give rise to surjective maps from large dynamical systems to smaller ones. One can view these surjections as a kind of "fast/slow" variable decompositions or as "abstractions" in the computer science sense of the word.; Comment: 37 pages. Major revision of arXiv:1008.5359 [math.DS]. Following referees' suggestions we made the paper more accessible for applied dynamicists

Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/10/2015 Português
Relevância na Pesquisa
67.111577%
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to a subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves observable functions on the state-space of a dynamical system [Koopman 1931, PNAS]. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear observations of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems [Williams et al. 2015, JNLS]. It remains an open challenge how to choose the right nonlinear observable functions to form a subspace where it is possible to obtain efficient linear reduced-order models. Here, we investigate the choice of observable functions for Koopman analysis. First, we note that to obtain a linear Koopman system that advances the original states, it is helpful to include these states in the observable subspace, as in DMD. We then categorize dynamical systems by whether or not there exists a Koopman-invariant subspace that includes the state variables as observables. In particular, we note that this is only possible when there is a single isolated fixed point...

Partial Dynamical Systems, Fell Bundles and Applications

Exel, Ruy
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/11/2015 Português
Relevância na Pesquisa
67.091406%
This is a book about Partial Actions and Fell Bundles with applications to C*-algebras generated by partial isometries. Here is the table of contents: 1-Introduction, 2-Partial actions, 3-Restriction and globalization, 4-Inverse semigroups, 5-Topological partial dynamical systems, 6-Algebraic partial dynamical systems, 7-Multipliers, 8-Crossed products, 9-Partial group representations, 10-Partial group algebras, 11-C*-algebraic partial dynamical systems, 12-Partial isometries, 13-Covariant representations of C*-algebraic dynamical systems, 14-Partial representations subject to relations, 15-Hilbert modules and Morita-Rieffel-equivalence, 16-Fell bundles, 17-Reduced cross-sectional algebras, 18-Fell's absorption principle, 19-Graded C*-algebras, 20-Amenability for Fell bundles, 21-Functoriality for Fell bundles, 22-Functoriality for partial actions, 23-Ideals in graded algebras, 24-Pre-Fell-bundles, 25-Tensor products of Fell bundles, 26-Smash product, 27-Stable Fell bundles as partial crossed products, 28-Globalization in the C*-context, 29-Topologically free partial actions, 30-Dilating partial representations, 31-Semigroups of isometries, 32-Quasi-lattice ordered groups, 33-C*-algebras generated by semigroups of isometries, 34-Wiener-Hopf C*-algebras...

Eventual nonsensitivity and tame dynamical systems

Glasner, Eli; Megrelishvili, Michael
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
67.16655%
In this paper we characterize tame dynamical systems and functions in terms of eventual non-sensitivity and eventual fragmentability. As a notable application we obtain a neat characterization of tame subshifts $X \subset \{0,1\}^{\mathbb Z}$: for every infinite subset $L \subseteq {\mathbb Z}$ there exists an infinite subset $K \subseteq L$ such that $\pi_{K}(X)$ is a countable subset of $\{0,1\}^K$. The notion of eventual fragmentability is one of the properties we encounter which indicate some "smallness" of a family. We investigate a "smallness hierarchy" for families of continuous functions on compact dynamical systems, and link the existence of a "small" family which separates points of a dynamical system $(G,X)$ to the representability of $X$ on "good" Banach spaces. For example, for metric dynamical systems the property of admitting a separating family which is eventually fragmented is equivalent to being tame. We give some sufficient conditions for coding functions to be tame and, among other applications, show that certain multidimensional analogues of Sturmian sequences are tame. We also show that linearly ordered dynamical systems are tame and discuss examples where some universal dynamical systems associated with certain Polish groups are tame.; Comment: 44 pages

Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

Gu, Anhui; Li, Yangrong
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/04/2014 Português
Relevância na Pesquisa
67.091406%
We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the existence of a unique pullback attractor for the first-order lattice dynamical systems with both deterministic non-autonomous forcing terms and multiplicative white noise. Our results recover many existing ones on the existences of pullback attractors for lattice dynamical systems with autonomous terms or white noises.

Consistency of maximum likelihood estimation for some dynamical systems

McGoff, Kevin; Mukherjee, Sayan; Nobel, Andrew; Pillai, Natesh
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
67.14241%
We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.; Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"

Bollt, Erik M.; Sun, Jie
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/05/2015 Português
Relevância na Pesquisa
67.15048%
This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported herein reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

On C*-algebras of irreversible algebraic dynamical systems

Stammeier, Nicolai
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
67.091406%
Extending the work of Cuntz and Vershik, we develop a general notion of independence for commuting group endomorphisms. Based on this concept, we initiate the study of irreversible algebraic dynamical systems, which can be thought of as irreversible analogues of the dynamical systems considered by Schmidt. To each irreversible algebraic dynamical system, we associate a universal C*-algebra and show that it is a UCT Kirchberg algebra under natural assumptions. Moreover, we discuss the structure of the core subalgebra, which is closely related to generalised Bunce-Deddens algebras in the sense of Orfanos. We also construct discrete product systems of Hilbert bimodules for irreversible algebraic dynamical systems which allow us to view the associated C*-algebras as Cuntz-Nica-Pimsner algebras. Besides, we prove a decomposition theorem for semigroup crossed products of unital C*-algebras by semidirect products of discrete, left cancellative monoids.; Comment: 41 pages

Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems

Mierczyński, Janusz; Shen, Wenxian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/11/2014 Português
Relevância na Pesquisa
67.09927%
This is the third part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general theory, developed in the authors' paper "Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory," Trans. Amer. Math. Soc. 365 (2013), pp. 5329-5365, to positive continuous-time random dynamical systems on infinite dimensional ordered Banach spaces arising from random parabolic equations and random delay systems. It is shown under some quite general assumptions that measurable linear skew-product semidynamical systems generated by random parabolic equations and by cooperative systems of linear delay differential equations admit measurable families of generalized principal Floquet subspaces, and generalized principal Lyapunov exponents.; Comment: 42 pages; submitted for publication

Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems

Mierczyński, Janusz; Shen, Wenxian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
67.08657%
This is the second part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general theory, developed in the authors' paper "Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory," Trans. Amer. Math. Soc., in press, to positive random dynamical systems on finite-dimensional ordered Banach spaces. It is shown under some quite general assumptions that measurable linear skew-product semidynamical systems generated by measurable families of positive matrices and by strongly cooperative or type-K strongly monotone systems of linear ordinary differential equations admit measurable families of generalized principal Floquet subspaces, generalized principal Lyapunov exponents, and generalized exponential separations.; Comment: 31 pages; some clarifications have been made, and minor typos corrected. Published in the Journal of Mathematical Analysis and Applications

Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory

Mierczyński, Janusz; Shen, Wenxian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
67.1582%
This is the first of a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. It focuses on the development of general theory. First, the notions of generalized principal Floquet subspaces, generalized principal Lyapunov exponents, and generalized exponential separations for general positive random dynamical systems in ordered Banach spaces are introduced, which extend the classical notions of principal Floquet subspaces, principal Lyapunov exponents, and exponential separations for strongly positive deterministic systems in strongly ordered Banach to general positive random dynamical systems in ordered Banach spaces. Under some quite general assumptions, it is then shown that a positive random dynamical system in an ordered Banach space admits a family of generalized principal Floquet subspaces, a generalized principal Lyapunov exponent, and a generalized exponential separation. We will consider in the forthcoming parts applications of the general theory developed in this part to positive random dynamical systems arising from a variety of random mappings and differential equations, including random Leslie matrix models, random cooperative systems of ordinary differential equations...

Kosambi-Cartan-Chern (KCC) theory for higher order dynamical systems

Harko, Tiberiu; Pantaragphong, Praiboon; Sabau, Sorin V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
67.25202%
The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system, with the solution curves of the dynamical system described by methods inspired by the theory of geodesics in a Finsler spaces. The evolution of a dynamical system is geometrized by introducing a non-linear connection, which allows the construction of the KCC covariant derivative, and of the deviation curvature tensor. In the KCC theory the properties of any dynamical system are described in terms of five geometrical invariants, with the second one giving the Jacobi stability of the system. Usually, the KCC theory is formulated by reducing the dynamical evolution equations to a set of second order differential equations. In the present paper we introduce and develop the KCC approach for dynamical systems described by systems of arbitrary $n$-dimensional first order differential equations. We investigate in detail the properties of the $n$-dimensional autonomous dynamical systems, as well as the relationship between the linear stability and the Jacobi stability. As a main result we find that only even-dimensional dynamical systems can exhibit both Jacobi stability and instability behaviors...

The steady states of coupled dynamical systems compose according to matrix arithmetic

Spivak, David I.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/12/2015 Português
Relevância na Pesquisa
67.24096%
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be arranged in series, in parallel, and with feedback to form a new dynamical system---this is called compositionality---and the process can be repeated in a fractal-like manner to form more complex systems of systems. One issue is that as larger systems are created, their state space grows exponentially. In this paper a technique for calculating the steady states of a system of systems, in terms of the steady states of its component dynamical systems, is provided. These are organized into "steady state matrices" which are strongly analogous to bifurcation diagrams. It is shown that the compositionality structure of dynamical systems fits with the familiar monoidal structure for the steady state matrices, where serial, parallel, and feedback composition of matrices correspond to multiplication, Kronecker product, and partial trace operations. The steady state matrices of dynamical systems respect this compositionality structure, exponentially reducing the complexity involved in studying the steady states of composite dynamical systems.; Comment: 40 pages

Cycle Equivalence of Graph Dynamical Systems

Macauley, Matthew; Mortveit, Henning S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/02/2008 Português
Relevância na Pesquisa
67.095566%
Graph dynamical systems (GDSs) can be used to describe a wide range of distributed, nonlinear phenomena. In this paper we characterize cycle equivalence of a class of finite GDSs called sequential dynamical systems SDSs. In general, two finite GDSs are cycle equivalent if their periodic orbits are isomorphic as directed graphs. Sequential dynamical systems may be thought of as generalized cellular automata, and use an update order to construct the dynamical system map. The main result of this paper is a characterization of cycle equivalence in terms of shifts and reflections of the SDS update order. We construct two graphs C(Y) and D(Y) whose components describe update orders that give rise to cycle equivalent SDSs. The number of components in C(Y) and D(Y) is an upper bound for the number of cycle equivalence classes one can obtain, and we enumerate these quantities through a recursion relation for several graph classes. The components of these graphs encode dynamical neutrality, the component sizes represent periodic orbit structural stability, and the number of components can be viewed as a system complexity measure.

Second order forward-backward dynamical systems for monotone inclusion problems

Bot, Radu Ioan; Csetnek, Ernö Robert
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/03/2015 Português
Relevância na Pesquisa
67.091406%
We begin by considering second order dynamical systems of the from $\ddot x(t) + \Gamma (\dot x(t)) + \lambda(t)B(x(t))=0$, where $\Gamma: {\cal H}\rightarrow{\cal H}$ is an elliptic bounded self-adjoint linear operator defined on a real Hilbert space ${\cal H}$, $B: {\cal H}\rightarrow{\cal H}$ is a cocoercive operator and $\lambda:[0,+\infty)\rightarrow [0,+\infty)$ is a relaxation function depending on time. We show the existence and uniqueness of strong global solutions in the framework of the Cauchy-Lipschitz-Picard Theorem and prove weak convergence for the generated trajectories to a zero of the operator $B$, by using Lyapunov analysis combined with the celebrated Opial Lemma in its continuous version. The framework allows to address from similar perspectives second order dynamical systems associated with the problem of finding zeros of the sum of a maximally monotone operator and a cocoercive one. This captures as particular case the minimization of the sum of a nonsmooth convex function with a smooth convex one and allows us to recover and improve several results from the literature concerning the minimization of a convex smooth function subject to a convex closed set by means of second order dynamical systems. When considering the unconstrained minimization of a smooth convex function we prove a rate of ${\cal O}(1/t)$ for the convergence of the function value along the ergodic trajectory to its minimum value. A similar analysis is carried out also for second order dynamical systems having as first order term $\gamma(t) \dot x(t)$...

Continuation of solutions of coupled dynamical systems

Chen, Tianping; Wu, Wei
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/08/2007 Português
Relevância na Pesquisa
67.111577%
Recently, the synchronization of coupled dynamical systems has been widely studied. Synchronization is referred to as a process wherein two (or many) dynamical systems are adjusted to a common behavior as time goes to infinity, due to coupling or forcing. Therefore, before discussing synchronization, a basic problem on continuation of the solution must be solved: For given initial conditions, can the solution of coupled dynamical systems be extended to the infinite interval $[0,+\infty)$? In this paper, we propose a general model of coupled dynamical systems, which includes previously studied systems as special cases, and prove that under the assumption of QUAD, the solution of the general model exists on $[0,+\infty)$.

Hyperbolic Dynamical Systems

Araujo, Vitor; Viana, Marcelo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/04/2008 Português
Relevância na Pesquisa
67.127363%
The theory of uniformly hyperbolic dynamical systems was initiated in the 1960's (though its roots stretch far back into the 19th century) by S. Smale, his students and collaborators, in the west, and D. Anosov, Ya. Sinai, V. Arnold, in the former Soviet Union. It came to encompass a detailed description of a large class of systems, often with very complex evolution. Moreover, it provided a very precise characterization of structurally stable dynamics, which was one of its original main goals. The early developments were motivated by the problem of characterizing structural stability of dynamical systems, a notion that had been introduced in the 1930's by A. Andronov and L. Pontryagin. Inspired by the pioneering work of M. Peixoto on circle maps and surface flows, Smale introduced a class of gradient-like systems, having a finite number of periodic orbits, which should be structurally stable and, moreover, should constitute the majority (an open and dense subset) of all dynamical systems. Stability and openness were eventually established, in the thesis of J. Palis. However, contemporary results of M. Levinson, based on previous work by M. Cartwright and J. Littlewood, provided examples of open subsets of dynamical systems all of which have an infinite number of periodic orbits.; Comment: 22 pages...