Comparative study of variational chaos indicators and ODEs' numerical integrators

• Autores: Darriba, Luciano A.; Maffione, Nicolás Pablo; Cincotta, Pablo M.; Giordano, Claudia M.
• Año de publicación: 2012
• Idioma: español castellano
• Tipo de recurso: artículo
• Materia: Astronomía; Chaos Indicators; Numerical Integrators; Variational Equations; ODEs; Hamil-tonian Systems; Astronomía
• Institución: Universidad Nacional de Río Negro

Fil: Darriba, Luciano A. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Darriba, Luciano A. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Darriba, Luciano A. Instituto de Astrofísica La Plata; Argentina
Fil: Maffione, Nicolas P. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Maffione, Nicolas P. Instituto de Astrofísica La Plata; Argentina
Fil: Maffione, Nicolas P. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Cincotta, Pablo M. Instituto de Astrofísica La Plata; Argentina
Fil: Cincotta, Pablo M. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata; Argentina
Fil: Cincotta, Pablo M. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Giordano, Claudia M. Instituto de Astrofísica de La Plata; Argentina.
Fil: Giordano, Claudia M. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Giordano, Claudia M. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
The reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of Maffione et al. (2011a) for mappings, a detailed comparison among the widespread indicators of chaos in a general system is still lacking. Such a comparison could lead to select the most efficient algorithms given a certain dynamical problem. Furthermore, in order to choose the appropriate numerical integrators to compute them, more comparative studies among numerical integrators are also needed. This work deals with both problems. We first extend the work of Maffione et al. (2011) for mappings to the 2D H\'enon & Heiles (1964) potential, and compare several variational indicators of chaos: the Lyapunov Indicator (LI); the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI) and its generalized version, the Generalized Alignment Index (GALI); the Fast Lyapunov Indicator (FLI) and its variant, the Orthogonal Fast Lyapunov Indicator (OFLI); the Spectral Distance (D) and the Dynamical Spectras of Stretching Numbers (SSNs). We also include in the record the Relative Lyapunov Indicator (RLI), which is not a variational indicator as the others. Then, we test a numerical technique to integrate Ordinary Differential Equations (ODEs) based on the Taylor method implemented by Jorba & Zou (2005) (called taylor), and we compare its performance with other two well-known efficient integrators: the Prince & Dormand (1981) implementation of a Runge-Kutta of order 7-8 (DOPRI8) and a Bulirsch-St\"oer implementation. These tests are run under two very different systems from the complexity of their equations point of view: a triaxial galactic potential model and a perturbed 3D quartic oscillator.