共查询到20条相似文献,搜索用时 562 毫秒
1.
This paper studies the initial value problem of multi-layer cellular neural networks. We demonstrate that the mosaic solutions of such system is topologically conjugated to a new class in symbolic dynamical systems called the path set (Abram and Lagarias in Adv Appl Math 56:109–134, 2014). The topological entropies of the solution, output, and hidden spaces of a multi-layer cellular neural network with initial condition are formulated explicitly. Also, a sufficient condition for whether the mosaic solution space of a multi-layer cellular neural network is independent of initial conditions is addressed. Furthermore, two spaces exhibit identical topological entropy if and only if they are finitely equivalent. 相似文献
2.
Tomasz Downarowicz L’ubomír Snoha Dariusz Tywoniuk 《Journal of Dynamics and Differential Equations》2017,29(1):243-257
There are two main subjects in this paper. (1) For a topological dynamical system \((X,T)\) we study the topological entropy of its “functional envelopes” (the action of \(T\) by left composition on the space of all continuous self-maps or on the space of all self-homeomorphisms of \(X\)). In particular we prove that for zero-dimensional spaces \(X\) both entropies are infinite except when \(T\) is equicontinuous (then both equal zero). (2) We call Slovak space any compact metric space whose homeomorphism group is cyclic and generated by a minimal homeomorphism. Using Slovak spaces we provide examples of (minimal) systems \((X,T)\) with positive entropy, yet, whose functional envelope on homeomorphisms has entropy zero (answering a question posed by Kolyada and Semikina). Finally, also using Slovak spaces, we resolve a long standing open problem whether the circle is a unique non-degenerate continuum admitting minimal continuous transformations but only invertible: No, some Slovak spaces are such, as well. 相似文献
3.
In this work, we introduce the notion of conductance in the context of Cuntz–Krieger C∗-algebras. These algebras can be seen as a noncommutative version of topological Markov chains. Conductance is a useful notion
in the theory of Markov chains to study the approach of a system to the equilibrium state. Our goal is twofold. On one hand,
conductance can be used to measure the complexity of dynamical systems, complementing topological entropy. On the other hand,
using C∗-algebras, we can give a natural framework to analyze the path space of a finite graph associated to a Markov shift. 相似文献
4.
K. Balachandran V. Govindaraj L. Rodríguez-Germá J. J. Trujillo 《Nonlinear dynamics》2013,71(4):605-612
The aim of this paper is to derive a set of sufficient conditions for controllability of nonlinear fractional dynamical system of order 1<α<2 in finite dimensional spaces. The results are obtained using the Schauder fixed point theorem. Examples are included to verify the result. 相似文献
5.
The repetition property of a dynamical system, a notion introduced in Boshernitzan and Damanik (Commun Math Phys 283:647–662, 2008), plays an importance role in analyzing spectral properties of ergodic Schrödinger operators. In this paper, entropy of dynamical systems with repetition property is investigated. It is shown that the topological entropy of dynamical systems with the global repetition property is zero. Minimal dynamical systems having both topological repetition property and positive topological entropy are constructed. This provides a class of ergodic Schrödinger operators with potentials generated by positive entropy minimal dynamical systems that, in contrast to common beliefs, admit no eigenvalues. 相似文献
6.
In experimental psychology, artificial grammars, generated by directed graphs, are used to test the ability of subjects to implicitly learn the structure of complex rules. We introduce the necessary notation and mathematics to view an artificial grammar as the sequence space of a dynamical system. The complexity of the artificial grammar is equated with the topological entropy of the dynamical system and is computed by finding the largest eigenvalue of an associated transition matrix. We develop the necessary mathematics and include relevant examples (one from the implicit learning literature) to show that topological entropy is easy to compute, well defined, and intuitive and, thereby, provides a quantitative measure of complexity that can be used to compare data across different implicit learning experiments. 相似文献
7.
We first present some sufficient conditions for the existence and the construction of a pullback exponential attractor for the continuous process (non-autonomous dynamical system) on Banach spaces and weighted spaces of infinite sequences. Then we apply our results to study the existence of pullback exponential attractors for first order non-autonomous differential equations and partly dissipative differential equations on infinite lattices with time-dependent coupled coefficients and time-dependent external terms in weighted spaces. 相似文献
8.
We show that a non-wandering dynamical system with the shadowing property is either equicontinuous or has positive entropy and that in this context uniformly positive entropy is equivalent to weak mixing. We also show that weak mixing together with the shadowing property imply the specification property with a special kind of regularity in tracing (a weaker version of periodic specification property). This in turn implies that the set of ergodic measures supported on the closures of orbits of regularly recurrent points is dense in the space of all invariant measures (in particular, invariant measures in such a system form the Poulsen simplex, up to an affine homeomorphism). 相似文献
9.
The paper is concerned with a dynamical formulation of a recently established shell theory capable to catch finite deformations and falls within the class of geometrically exact shell theories. A basic aspect is the design of time integration schemes which preserve specific features of the continuous system such as conservation of momentum, angular momentum, and energy when the applied forces allow to. The integration method differs from the one recently proposed by Simo and Tarnow in being applicable without modifications to shell formulations with linear as well as nonlinear configuration spaces and in being independent of the nonlinearities involved in the strain-displacement relations. A finite element formulation is presented and various examples of nonlinear shell dynamics including large overall and chaotic motions are considered. 相似文献
10.
J. A. Tenreiro Machado 《Nonlinear dynamics》2010,62(1-2):371-378
This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems. 相似文献
11.
Weak Attractor for a Dissipative Euler Equation 总被引:1,自引:0,他引:1
A two-dimensional dissipative Euler equation is considered. We proved the existence of a global attractor in a weak sense, for the corresponding shift dynamical system in path space. 相似文献
12.
Roland Duduchava Ralf Kirsch Sergej Rjasanow 《Journal of Mathematical Fluid Mechanics》2006,8(2):242-266
We present new estimates of the Boltzmann collision operator in weighted Lebesgue and Bessel potential spaces. The main focus
is put on hard potentials under the assumption that the angular part of the collision kernel fulfills some weighted integrability
condition. In addition, the proofs for some previously known
-estimates have been considerably shortened and carried out by elementary methods. For a class of metric spaces, the collision
integral is seen to be a continuous operator into the same space.
Furthermore, we give a new pointwise lower bound as well as asymptotic estimates for the loss term without requiring that
the entropy is finite. 相似文献
13.
针对一类非线性系统提出了一种新的载荷识别方法,组合迭代法.该方法通过有限元方法和主动控制方法组合迭代来实现一类非线性系统的载荷识别.首先将非线性系统的有限元模型模态缩减成简化模型,由简化模型组成主动控制的被控对象;然后在选定的控制律下,设计控制调节器,使该系统监测点的响应功率谱密度达到预定谱,从而得到系统激励,即被识别的载荷;最后由非线性有限元响应验证载荷的合理性.对圆锥壳-包带组合系统载荷识别的数值研究表明了组合迭代法的有效性.该方法为导弹、宇宙飞船、航天飞机、火箭等航天航空结构振动试验的载荷识别提供指导作用,将促进航天航空事业的发展. 相似文献
14.
Nonlinear Dynamics - We develop a new cross-sample entropy, namely the multiscale cross-trend sample entropy (MCTSE), to investigate the synchronism of dynamical structure regarding two series with... 相似文献
15.
S. V. Zelik 《Journal of Dynamics and Differential Equations》2007,19(1):1-74
We consider in this article a nonlinear reaction–diffusion system with a transport term (L,∇
x
)u, where L is a given vector field, in an unbounded domain Ω. We prove that, under natural assumptions, this system possesses a locally compact attractor
in the corresponding phase space. Since the dimension of this attractor is usually infinite, we study its Kolmogorov’s ɛ-entropy and obtain upper and lower bounds of this entropy. Moreover, we give a more detailed study of the spatio-temporal chaos generated by the spatially homogeneous RDS in
. In order to describe this chaos, we introduce an extended (n + 1)-parametrical semigroup, generated on the attractor by 1-parametrical temporal dynamics and by n-parametrical group of spatial shifts ( = spatial dynamics). We prove that this extended semigroup has finite topological entropy, in contrast to the case of purely temporal or purely spatial dynamics, where the topological entropy is infinite. We also modify the concept of topological entropy in such a way that the modified one is finite and strictly positive, in particular for purely temporal and for purely spatial dynamics on the attractor. In order to clarify the nature of the spatial and temporal chaos on the attractor, we use (following Zelik, 2003, Comm. Pure. Appl. Math. 56(5), 584–637) another model dynamical system, which is an adaptation of Bernoulli shifts to the case of infinite entropy and construct homeomorphic embeddings of it into the spatial and temporal dynamics on
. As a corollary of the obtained embeddings, we finally prove that every finite dimensional dynamics can be realized (up to a homeomorphism) by restricting the temporal dynamics to the appropriate invariant subset of
. 相似文献
16.
Yanni Zeng 《Archive for Rational Mechanics and Analysis》2010,196(1):191-225
We study gas flows with any finite number of thermal nonequilibrium modes. The equations describing such flows are a hyperbolic
system with several relaxation equations. An important feature is entropy increase dictated by physics for any irreversible
process. Under physical assumptions we obtain properties of thermodynamic variables relevant to stability. By the energy method
we prove global existence and uniqueness for the Cauchy problem when the initial data are small perturbations of constant
equilibrium states. We give a precise formulation of the fundamental solution for the linearized system, and use it to obtain
large time behavior of solutions to the nonlinear system. In particular, we show that the entropy increases but stays bounded.
The resulting asymptotic picture of nonequilibrium flows is in a pointwise sense both in space and in time. 相似文献
17.
This paper analyzes dynamical behavior of a simply supported Euler?CBernoulli beam with a time-varying mass on its surface. Though the system under consideration is linear, it exhibits dynamics similar to a nonlinear system behavior including internal resonances. The asymptotical solutions for the beam displacement has been found by combining the classical Galerkin method with the averaging method for equations in Banach spaces. The resonance conditions have been derived. It has been proposed a method for finding a number of possible resonances.Effect of the beam parameters on its dynamical behavior is investigated as well. 相似文献
18.
The classical Fokker–Planck equation is a linear parabolic equation which describes the time evolution of the probability
distribution of a stochastic process defined on a Euclidean space. Corresponding to a stochastic process, there often exists
a free energy functional which is defined on the space of probability distributions and is a linear combination of a potential
and an entropy. In recent years, it has been shown that the Fokker–Planck equation is the gradient flow of the free energy
functional defined on the Riemannian manifold of probability distributions whose inner product is generated by a 2-Wasserstein
distance. In this paper, we consider analogous matters for a free energy functional or Markov process defined on a graph with
a finite number of vertices and edges. If N ≧ 2 is the number of vertices of the graph, we show that the corresponding Fokker–Planck equation is a system of N
nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. However, in contrast to stochastic
processes defined on Euclidean spaces, the situation is more subtle for discrete spaces. We have different choices for inner
products on the space of probability distributions resulting in different Fokker–Planck equations for the same process. It
is shown that there is a strong connection but there are also substantial discrepancies between the systems of ordinary differential
equations and the classical Fokker–Planck equation on Euclidean spaces. Furthermore, both systems of ordinary differential
equations are gradient flows for the same free energy functional defined on the Riemannian manifolds of probability distributions
with different metrics. Some examples are also discussed. 相似文献
19.
The existence of a compact uniform attractor for a family of processes corresponding to the dissipative non-autonomous Klein-Gordon-Schrodinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established. 相似文献