In this paper, we investigate the continuity of attractors in time-dependent phase spaces. (i) We establish two abstract criteria on upper semicontinuity and residual pullback D-attractor with respect to perturbations, an equivalence criterion between their equi-attraction, which generalize theory developed recently [27], [28] that (ii) propose notion D-exponential attractor, includes exponenti...

[1] Leaf area is the most relevant scalar variable for describing the dynamics of vegetation on seasonal time scales, and hence is required as part of the land-surface component of a meteorological model. A mathematical scheme for the dynamic vegetation component of such a model is formulated and reduced to a toy model for seasonal leaf dynamics. Leaf growth is seen as a temperature-initiated i...

Recordings in awake, behaving animals demonstrate that cells in medial entorhinal cortex (mEC) show "grid cell" firing activity when a rat explores an open environment. Intracellular recording in slices from different positions along the dorsal to ventral axis show differences in intrinsic properties such as subthreshold membrane potential oscillations (MPO), resonant frequency, and the presenc...

As can be represented by neurons and their synaptic connections, attractor networks are widely believed to underlie biological memory systems and have been used extensively in recent years to model the storage and retrieval process of memory. In this paper, we propose a new energy function, which is nonnegative and attains zero values only at the desired memory patterns. An attractor network is...

Before the advent of modern computers, mathematicians used analog circuits to model non-integrable differential equations. This paper investigates the feasibility, functionality, and accuracy of several systems including the solar system, three-body system, and Lorenz attractor. Due to their highly nonlinear nature and circuit limitations, the solar system and three-body systems are not practic...

Based on dilatonic dark energy model, we consider two cases: dilaton field with positive kinetic energy(coupled quintessence) and with negative kinetic energy(phantom). In the two cases, we investigate the existence of attractor solutions which correspond to an equation of state parameter ω = −1 and a cosmic density parameter Ωσ = 1. We find that the coupled term between matter and dilaton can’...

We consider a deconvolution model for 3D periodic flows. We show the existence of a global attractor for the model. MCS Classification : 76D05, 35Q30, 76F65, 76D03 Key-words : Navier-Stokes equations, Large eddy simulation, Deconvolution models.

We investigate a simple model of structured attractor neural network (ANN). In this network a module codes for the category of the stored information, while another

We study the phenomenology of Higgs-Dilaton model in context Einstein-Cartan gravity, focusing on separate impact Holst and Nieh-Yan terms inflationary observables. Using analytical numerical techniques, we show predictions these scenarios to display an attractor-like behaviour intrinsically related curvature field-space manifold metric formulation theory. Beyond that, analysis case reveals exi...