Authors:
Carlos Argáez
1
;
Peter Giesl
2
and
Sigurdur Freyr Hafstein
1
Affiliations:
1
Science Institute, University of Iceland, Dunhagi 5, 107 Reykjavík and Iceland
;
2
Peter Giesl is with the Department of Mathematics, University of Sussex, Falmer, BN1 9QH and U.K.
Keyword(s):
Lyapunov Functions, Chain-recurrent Set, Programming, Algorithm, Mathematics, Dynamical Systems.
Related
Ontology
Subjects/Areas/Topics:
Dynamical Systems Models and Methods
;
Formal Methods
;
Mathematical Simulation
;
Non-Linear Systems
;
Simulation and Modeling
Abstract:
Describing dynamical systems requires capability to isolate periodic behaviour. In Lyapunov’s theory, the qualitative behaviour of a dynamical system given by a differential equation can be described by a scalar function that decreases along solutions: the Complete Lyapunov Function. The chain-recurrent set will produce constant values of an associated complete Lyapunov function and zero values of its orbital derivative. Recently, we have managed to isolate the chain-recurrent set of different dynamical systems in 2- and 3-di- mensions. An overestimation, however, is always obtained. In this paper, we present a method to reduce such overestimation based on geometrical middle points for 2-dimensional systems.