Theory and applications of the orthogonal Fast Lyapunov indicator (OFLI and OFLI2)methods

Abstract

During the last decades the Nonlinear Dynamics field has produced a large number of numerical techniques oriented to the analysis of the behavior of the orbits in different systems. These methods are mainly focused to distinguish chaotic from regular behavior. Among the variational methods, based into the variational equations, we discuss in this paper the so-called Orthogonal Fast Lyapunov Indicator (OFLI and OFLI2) methods that are variants of the FLI method but designed to obtain also some information about the periodic orbits of the systems. We review the OFLI and OFLI2 methods and we show several computational aspects related with avoiding the appearance of spurious structures, with their use in the analysis of regular/chaotic behaviors, but also with the analysis of periodic orbits and regular regions, and with the efficient computation of the solution of the variational equations by means of Taylor series methods. Finally, the methods are shown in several Hamiltonian problems, as well as in several classical dissipative systems, as the Lorenz and Rössler models.