Authors:
Carlos Argáez
1
;
Peter Giesl
2
and
Sigurdur Hafstein
1
Affiliations:
1
Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland
;
2
Department of Mathematics, University of Sussex, Falmer, BN1 9QH, U.K.
Keyword(s):
Complete Lyapunov Functions, Chain-recurrent Set, Numerical Methods, Dynamical Systems, Iterative Methods.
Abstract:
A complete Lyapunov function determines the behaviour of a dynamical system. In particular, it splits the phase space into the chain-recurrent set, where solutions show (almost) repetitive behaviour, and the part exhibiting gradient-like flow where the dynamics are transient. Moreover, it reveals the stability of sets and basins of attraction through its sublevel sets. In this paper, we combine two previous methods to compute complete Lyapunov functions: we employ quadratic optimization with equality and inequality constraints to compute a complete Lyapunov function candidate and we evaluate its quality by using a method that improves approximations of complete Lyapunov function candidates through iterations.