(h, k)-trichotomies and asymptotics of nonautonomous difference systems

Nonautonomous difference equations: Open problems and conjectures

On the shadowing property of nonautonomous discrete systems

In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of  weak contractions with shadowing and h-shadowing property.

Periodicity Detection in Nonautonomous Difference Equations

System identification for nonlinear differential and difference equations has lagged far behind the linear case, due to the greater complexity of the task. Takens’ Theorem [1,10] of 25 years ago opened a new avenue of investigation, introducing geometric methods that were essential for nonlinear problems. The ramifications of this result have unfolded in an area that has become known as attract...

$k$-Total difference cordial graphs

Let $G$ be a graph. Let $f:V(G)to{0,1,2, ldots, k-1}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $left|f(u)-f(v)right|$. $f$ is called a $k$-total difference cordial labeling of $G$ if $left|t_{df}(i)-t_{df}(j)right|leq 1$, $i,j in {0,1,2, ldots, k-1}$ where $t_{df}(x)$ denotes the total number of vertices and the edges labeled with $x$.A graph with admits a...

Analysis of Nonautonomous Adversarial Systems

Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for stabilizing training of GANs, β-GAN was the first who proposed a complete anne...