Dynamical systems describe the evolution of quantities governed by differential equations.
Hence, they represent a very powerful prediction tool in many disciplines such as physics …

Complete Lyapunov functions are of much interest in control theory because of their
capability to describe the long-time behaviour of nonlinear dynamical systems. The state …

The CPA method to compute Lyapunov functions depends on a triangulation of the relevant
part of the state space. In more detail, a CPA (Continuous and Piecewise Affine) function is …

A complete Lyapunov function characterizes the behaviour of a general dynamical system.
In particular, the state space is split into the chain-recurrent set, where the function is …

The existence of a smooth Lyapunov function for any smooth planar dynamical system with
one limit cycle is proved, which is based on a novel decomposition of the dynamical system …

A complete Lyapunov function describes the qualitative behaviour of a dynamical system:
the areas where the orbital derivative vanishes and where it is strictly negative characterise …

Meshfree collocation in reproducing kernel Hilbert spaces is an established method to solve
generalized interpolation problems such as PDEs. It can be formulated as an optimization …

Differential equations describe many interesting phenomena arising from various
disciplines. This includes many important models, eg predator-prey in population biology or …

When studying the behaviour of dynamical systems, one particular goal is to find and isolate
the periodic solutions and the equilibria. They are a subset of the chain-recurrent set of the …

LyapXool is a C++ program to compute complete Lyapunov functions and their orbital
derivatives for any two-or three-dimensional dynamical system expressed by an …