Authors:
Carlos Argáez
1
;
Peter Giesl
2
and
Sigurdur Hafstein
1
Affiliations:
1
Science Institute, University of Iceland, VR-III, 107 Reykjavík and Iceland
;
2
Department of Mathematics, University of Sussex and U.K.
Keyword(s):
Dynamical System, Complete Lyapunov Function, Orbital Derivative, Meshless Collocation, Radial Basis Functions.
Related
Ontology
Subjects/Areas/Topics:
Dynamical Systems Models and Methods
;
Formal Methods
;
Mathematical Simulation
;
Non-Linear Systems
;
Simulation and Modeling
Abstract:
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 and engineering, chemistry and biology and even in economics, among others. Their importance relies on their capability of predicting, as a function of time, future states of the corresponding system under consideration by means of the current, known state. Many difficulties arise when trying to solve such systems. Complete Lyapunov functions allow for the systematic study of complicated dynamical systems. In this paper, we present a new iterative algorithm that avoids obtaining trivial solutions when constructing complete Lyapunov functions. This algorithm is based on mesh-free numerical approximation and analyzes the failure of convergence in certain areas to determine the chain-recurrent set.