Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both
in theory and applications. They provide sufficient conditions for the stability of equilibria or …

This book combines two mathematical branches: dynamical systems and radial basis
functions. It is mainly written for mathematicians with experience in at least one of these two …

The stability and basin of attraction of an equilibrium can be determined by a contraction
metric. A contraction metric is a Riemannian metric with respect to which the distance …

A Riemannian metric with a local contraction property can be used to prove existence and
uniqueness of a periodic orbit and determine a subset of its basin of attraction. While the …

In this article, new concepts of (exponential) attractivity for nonautonomous differential
equations on a finite time interval are introduced. Due to nonuniqueness of finite-time …

Contraction analysis uses a local criterion to prove the long-term behavior of a dynamical
system. We consider a contraction metric, ie, a Riemannian metric with respect to which the …

The dynamics of many systems from physics, economics, chemistry, and biology can be
modelled through polynomial functions. In this paper, we provide a computational means to …

The stability and the basin of attraction of a periodic orbit can be determined using a
contraction metric, ie, a Riemannian metric with respect to which adjacent solutions contract …

называется к о н е ч н о й в р е м е н н ó й труба кой длины 2λ динамической системы
(1), поа строенной на множестве M. О п р е д е л е н и е 1.3. Замкнутое в Φ множеа ство …

The determination of the basin of attraction of a periodic orbit can be achieved using a
Lyapunov function. A Lyapunov function can be constructed by approximation of a first-order …