Dynamic System

The integrable coupled nonlinear Schrödinger equation of Manakov type is widely used in recent developments in the field of optical solitons in fibers. The use and applications of the equation is to explain how the solitons waves transmit in optical fiber, what happens when the ...

The integrable coupled nonlinear Schrödinger equation of Manakov type is widely used in recent developments in the field of optical solitons in fibers. The use and applications of the equation is to explain how the solitons waves transmit in optical fiber, what happens when the ...

The integrable coupled nonlinear Schrödinger equation of Manakov1 type is widely used in recent developments in the field of optical solitons in fibers. The use and applications of the equation is to explain how the solitons waves transmit in optical fiber, what happens when the ...

Symbolic reasoning about continuous dynamic systems requires consistent qualitativeabstraction functions and a consistent symbolic model. Classically, symbolic reasoningsystems have utilized a box partition of the system space to achieve qualitative abstraction,but boxes can not provide a consistent abstraction. Our Q2methodology abstracts aprovably consistent symbolic representation of noise-free general dynamic systems.However the Q2symbolic representation has not been previously ...

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of n variables, K:[0,1]n→ℝ, which are separately Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We also present applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.

Let Σ be a finite alphabet, Ω=Σℤd equipped with the shift action, and ℐ the simplex of shift-invariant measures on Ω. We study the relation between the restriction ℐn of ℐ to the finite cubes {−n,…,n}d⊂ℤd, and the polytope of ‘locally invariant’ measures ℐlocn. We are especially interested in the geometry of the convex set ℐn, which turns out to be strikingly different when d=1 and when d≥2 . A major role is played by shifts of finite type which are naturally identified with faces of ℐn, and uniquely ergodic shifts of finite type, whose unique invariant measure gives rise to extreme points of ℐn, although in dimension d≥2 there are also extreme points which arise in other ways. We show that ℐn =ℐlocn when d=1 , but in higher dimensions they differ for n large enough. We also show that while in dimension one ℐn are polytopes with rational extreme points, in higher dimensions every computable convex set occurs as a rational image of a face of ℐn for all large enough n.

We present the domain specific programming language MGS and its approach to the specification of dynamical systems with a dynamical structure or (DS)2. MGS stands for "encore un Modele General de Simulation", that is, "yet another general model of simulation". Its declarative approach is based on the notions of chains and cochains well studied in algebraic topology. A careful discussion of the design goals lead us to relax some of the constraints on these mathematical structures to represent in a uniform way various data structures and transformations. In particular, our computational notion of transformation relies on a rewriting mechanism encompassing the usual notions of set, string and term rewriting. These notions are illustrated on two examples involving the implicit computation of a time varying neighborhood: the simulation of the trajectories of flocking birds and the growth of an epithelial tissue. The second example illustrates also the compositionality...

Abstract. We propose a new approach to superrigidity phenomena and im-plement it for lattice representations and measurable cocycles with Homeo+(S1) as the target group. We are motivated by Ghys' theorem stating that any rep-resentation ̺ : Γ → Homeo+(S1) of an irreducible ...

Solution of non-linear dynamic systems is dependent on exact knowledge of the initial conditions. Even a slight deviation of these values can cause substantial change in the overall course of the event. It then appears chaotic. Development of such dynamic system can be represented using abstract phase space through attractors, fractals, etc. A typical example is Lorenz attractor, which is in a three-dimensional view shaped as two intertwined spirals. Rössler attractor is a relatively simple system on which chaos in geometric form can be shown in a time sequence. Among the non-traditional oscillators in non-linear mechanics can be classified Duffing and Van der Pol oscillators. This paper shows an example of a chaotic attractor formed in a non-periodic mode, obtained in an experiment of water dripping from an unclosed valve.

The Hubbard model of strongly correlated electron systems is considered near half-filling within the framework of a new functional integral method without slave bosons. A dynamical system of equations determining the superconducting phase of the Hubbard model is derived. Both singlet and triplet Cooper pairings are studied.