Abstract: In analyzing large scale nonlinear dynamical systems,
it is often desirable to treat the overall system as a collection of
interconnected subsystems. Solutions properties of the large scale
system are then deduced from the solution properties of the
individual subsystems and the nature of the interconnections. In this
paper a new approach is proposed for the stability analysis of large
scale systems, which is based upon the concept of vector Lyapunov
functions and the decomposition methods. The present results make
use of graph theoretic decomposition techniques in which the overall
system is partitioned into a hierarchy of strongly connected
components. We show then, that under very reasonable assumptions,
the overall system is stable once the strongly connected subsystems
are stables. Finally an example is given to illustrate the constructive
methodology proposed.
Abstract: Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.