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 ...

*Correspondence: [email protected] 1Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, P.R. China Full list of author information is available at the end of the article Abstract In this paper, proving the pullback asymptotic compactness of processes by the aid of a contractive function in space X0, we prove the existence of a pullback attractor for N-dimensional non...

valdis laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. in this paper we introduce a new property of acts over monoids, called u-wpf which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. we also show that regu...