In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 1 0 of the cocycle ass...

The existence of a pullback attractor is established for the singularly perturbed FitzHughNagumo system defined on the entire space Rn when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system is proved by using uniform a priori estimates for far-field values of solutions. Although the limiting system has no global attractor, we show that the pullback...

BACKGROUND True 3D reconstruction of coronary arteries in patients based on intravascular ultrasound (IVUS) may be achieved by fusing angiographic and IVUS information (ANGUS). The clinical applicability of ANGUS was tested, and its accuracy was evaluated quantitatively. METHODS AND REUSLTS: In 16 patients who were investigated 6 months after stent implantation, a sheath-based catheter was used...

A nonautonomous or cocycle dynamical system that is driven by an autonomous dynamical system acting on a compact metric space is assumed to have a uniform pullback attractor. It is shown that discretization by a one-step numerical scheme gives rise to a discrete time cocycle dynamical system with a uniform pullback attractor, the component subsets of which converge upper semi continuously to th...

In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.

The aim of this paper is an extension of the theory of graph transformation systems in order to make them suitable for the speciication of reactive systems. For this purpose two main extensions of the algebraic theory of graph transformations are proposed. Firstly, graph transitions are introduced as a loose interpretation of graph productions, deened using a double pullback construction in con...

In distribution theory the pullback of a general distribution by a C∞function is well-defined whenever the normal bundle of the C∞-function does not intersect the wavefront set of the distribution. However, the Colombeau theory of generalized functions allows for a pullback by an arbitrary c-bounded generalized function. It has been shown in previous work that in the case of multiplication of C...

Recent work in action recognition has exposed the limitations of methods which directly classify local features extracted from spatio-temporal video volumes. In opposition, encoding the actions’ dynamics via generative dynamical models has a number of desirable features when it comes to unsupervised learning of plots, crowd monitoring, and description of more complex activities. However, using ...

2 Perturbed dynamics of parametrized systems 7 2.1 The inflation of cocycle dynamics . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Inflation through differential inclusions . . . . . . . . . . . . . . . . . 7 2.1.2 Inflation through additive controls . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Inflation through chain–connectedness . . . . . . . . . . . . . . . . . 8 2.2 Inflated p...