首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
Chaos synchronization in coupled systems is often characterized by a map phi between the states of the components. In noninvertible systems, or in systems without inherent symmetries, the synchronization set--by which we mean graph(phi)--can be extremely complicated. We identify, describe, and give examples of several different complications that can arise, and we link each to inherent properties of the underlying dynamics. In brief, synchronization sets can in general become nondifferentiable, and in the more severe case of noninvertible dynamics, they might even be multivalued. We suggest two different ways to quantify these features, and we discuss possible failures in detecting chaos synchrony using standard continuity-based methods when these features are present.  相似文献   

2.
In this paper we extract and highlight some essential ingredients and properties that characterize the phenomenon of anticipated synchronization when external additive noise sources perturb the master and slave dynamics. Our results rely on a minimal scalar setup able to exhibit the more fundamental aspects of this phenomenon, where the fluctuations around the average dynamics are worked out in a small noise and adiabatic approximations allowing to describe their dynamics through linear delay Langevin equations. In this context, we find necessary conditions that guarantee anticipated synchronization in the mean value. Fluctuations around this condition are studied through the stationary correlation of the delayed difference between the master and slave dynamics. It is shown that external noise properties can be inferred by measuring this object. Conditions for minimizing the dynamical fluctuations around the anticipated synchronization in mean value are found. A detailed analysis of the dependence on the characteristic parameters is presented.  相似文献   

3.
This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results.  相似文献   

4.
Given a Poisson (or more generally Dirac) manifold PP, there are two approaches to its geometric quantization: one involves a circle bundle QQ over PP endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of PP. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of PP is obtained from the Lie groupoid of QQ via an S1S1 reduction that preserves both the Lie groupoid and the geometric structures.  相似文献   

5.
We analyse the geometry of a thin knotted string with bending rigidity. Two types of geometric properties are investigated. First, following the approach of von der Mosel [H. von der Mosel, Asymptotic Anal. 18, 49 (1998)], we derive upper bounds for the multiplicity of crossings and braids. Then, using a general inequality for the length of 3D curves derived by Chakerian [G.D. Chakerian, Proc. of the American Math. Soc. 15, 886 (1964)], we analyze the size and confinement of a knot  相似文献   

6.
This note examines the geometry behind the Hamiltonian structure of isomonodromy deformations of connections on vector bundles over Riemann surfaces. The main point is that one should think of an open set of the moduli of pairs (V,∇)(V,) of vector bundles and connections as being obtained by “twists” supported over points of a fixed vector bundle V0V0 with a fixed connection 00; this gives two deformations, one, isomonodromic, of (V,∇)(V,), and another induced from the isomonodromic deformation of (V0,0)(V0,0). The difference between the two will be Hamiltonian.  相似文献   

7.
8.
9.
The orbit space of the Lorentz group acting on the product ofn real, or complex, Minkowski spaces is stratified into subspaces isomorphic to certain products of Grassmann manifolds and varieties of Gram matrices. The Lorentz orbits (of nonzero dimension) are completely classified by the Stiefel manifolds of standard orthogonal bases for the linear subspaces of the Minkowski space. Several representations of the spaces ofn-point Lorentz invariant distributions and differentiable, or analytic, functions onto appropriate spaces of distributions and functions of Lorentz invariant variables are also discussed.On leave of absence from the Institute of Atomic Physics, Bucharest, Romania.  相似文献   

10.
We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.  相似文献   

11.
This paper shows that general relativity and ordinary continuum models of matter imply the presence of Cartan torsion. The key concept is that torsion can be viewed as translational holonomy per unit area, in the limit of very small areas. Translational holonomy is introduced as the nonclosure of the development of a space-time loop into a flat space-time. The translational holonomy around a charged rotating black hole is calculated. If a large collection of small rotating objects is approximated by continuous spinning matter, the resulting torsion and spin have the same relation as in Einstein-Cartan theory, except that the torsion traces remain zero for the simple model of spinning matter used here. Finally, this construction adds torsion to the list of nonpropagating fields which can be viewed as continuum density of holonomy around localized space-time boundaries, or around throats which are connected to further local topological structures.  相似文献   

12.
We discuss the deformed sigma-model that arises when considering four-dimensional N=2N=2 abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry by non-holomorphic terms. We analyze the geometry of the sigma-model in terms of intrinsic torsion classes. We show that, generically, the deformed geometry is non-Kähler. We illustrate our findings with an example. We also express the deformed sigma-model in terms of the Hesse potential that underlies the real formulation of special geometry.  相似文献   

13.
This paper deals with the construction of “magnetic vorticity” vector using Greenberg's theory of spacelike congruences for the trajectories of magnetic fields. A set of propagation equations is derived for the geometrical invariants associated with the congruences of magnetic field lines and fluid flow lines. Some applications of these propagation equations are made. A generalization of Ferraro's law of isorotation is obtained employing the propagation equation forω 2 along the magnetic field lines.  相似文献   

14.
We discuss the asymptotic complete phase-frequency synchronization for the Kuramoto phase model with a finite size N. We present sufficient conditions for initial configurations leading to the exponential decay toward the completely synchronized states. Our new sufficient conditions and decay rate depend only on the coupling strength and the diameter of initial phase and natural frequency configurations. But they are independent of the system size N, hence they can be used for the mean-field limit. For the complete synchronization estimates, we estimate the time evolution of the phase and frequency diameters for configurations. The initial phase configurations for identical oscillators located on the half circle will converge to the complete synchronized states exponentially fast. In contrast, for the non-identical oscillators, the complete frequency synchronization will occur exponentially fast for some restricted class of initial phase configurations. Our estimates are based on the monotonicity arguments of extremal phase and frequencies, which do not employ any linearization procedure of nonlinear coupling terms and detailed information on the eigenvalue of the linearized system around the complete synchronized states. We compare our analytical results with numerical simulations.  相似文献   

15.
The formula for the size at the generalized ergosphere given by Denardo and Ruffini for the Reissner-Nordtstrøm metric is shown to apply in complete generality to the case of any black hole. The structure of the ergosurface is discussed and analytic formulae are given for various asymptotic limits.  相似文献   

16.
A preliminary investigation of global properties of the Stephani solution of the Einstein field equations is presented. This solution generalizes those of Friedman-Robertson-Walker (FRW) in such a way that the spatial curvature indexk (a constant in the FRW models) is a function of the time coordinate. The de Sitter solution, which is also a special case of the Stephani solution, is analyzed in the Stephani coordinates to gain insight into the global structure of the manifold and its foliation. The general metric is found to have several properties in common with this example. It has singularities which can be avoided either by matching the solution to an (as yet unknown) empty-space solution or confining the curvature index to be positive at all times.  相似文献   

17.
18.
We study the 3-form flux associated with the semi-classical geometry of G/H gauged Wess-Zumino-Witten models. We derive a simple, general expression for the flux in an orthonormal frame and use it to explicitly verify conformal invariance to the leading order in . For supersymmetric models, we briefly revisit the conditions for enhanced supersymmetry. We also discuss some examples of non-abelian cosets with flux.  相似文献   

19.
20.
The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated wave function. But it is concluded that the Bohm theory is not dynamically complete because the particle and its associated wave function do not satisfy the AR principle.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号