Asymptotic behavior of non-autonomous lattice systems

Non-Autonomous Systems: Asymptotic Behaviour and Weak Invariance Principles

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter N and variable area, associating a weight exp[pA− Jb] to a polygon with area A and b bends. For convex and column-convex polygons, we show that 〈A〉/Amax = 1−K(J)/p̃ 2 + O(ρ), where p̃ = pN ≫ 1, and ρ < 1. The constant K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons sh...

Asymptotic Behavior of Solutions to a Class of Linear Non-autonomous Neutral Delay Differential Equations

We study a class of linear non-autonomous neutral delay differential equations, and establish a criterion for the asymptotic behavior of their solutions, by using the corresponding characteristic equation.

Asymptotic Stability Theorem for Autonomous Systems

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Asymptotic behavior of impulsive non-autonomous delay difference equations with continuous variables

* Correspondence: danhuahe@zisu. edu.cn Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310012, P. R. China Full list of author information is available at the end of the article Abstract In this article, a class of impulsive non-autonomous delay difference equations with continuous variables is considered. By establishing a delay difference inequality with impul...