This chapter is intended as an introduction or tutorial to nonlinear dynamical systems in one and two dimensions with an emphasis on keeping the mathematics as elementary as possible. By its nature such an approach does not have the mathematical rigor that can be found in most textbooks dealing with this topic. On the other hand it may allow readers with a less extensive background in math to d...

In this paper we show how to compute the reachable space for uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on Taylor series and interval analysis. The second one relies on the theory of monotone dynamical systems and can be us...

The theory of differential equations has been widely known and developed in recent years. One the issues that many authors give their undivided attention to is stability boundary nonlinear dynamical systems. In this work, we first review several properties equilibrium points on boundary. We next extend characteristics for a fairly large class These are key completely determine

In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.