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LD1084D2T 其他数据使用手册 - ST Microelectronics（意法半导体）
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arXiv:1205.0875v3 [nlin.CD] 8 May 2012
May 9, 2012 0:59 ldarriba˙Review2010DDays
International Journal of Bifurcation and Chaos
c
World Scientific Publishing Company
Comparative study of variatio nal chaos indicato r s and ODEs’
numerical integrators
L.A. DARRIBA
Grupo de Caos en Sistemas Hamiltonianos
Facultad de Ciencias Astron´omicas y Geof´ısicas, Instituto de Astrof´ısica de La Plata, Universidad
Nacional de La Plata, CONICET-CCT La Plata,
Paseo del Bosque s/n, La Plata, B1900FWA, Bue nos Aire s, Argentina
ldarriba@f caglp.unlp.edu.ar
N.P. MAFFIO NE
Grupo de Caos en Sistemas Hamiltonianos
Facultad de Ciencias Astron´omicas y Geof´ısicas, Instituto de Astrof´ısica de La Plata, Universidad
Nacional de La Plata, CONICET-CCT La Plata,
Paseo del Bosque s/n, La Plata, B1900FWA, Bue nos Aire s, Argentina
nmaffione@fcaglp.unlp.edu.ar
P.M. CINCOTTA
Grupo de Caos en Sistemas Hamiltonianos
Facultad de Ciencias Astron´omicas y Geof´ısicas, Instituto de Astrof´ısica de La Plata, Universidad
Nacional de La Plata, CONICET-CCT La Plata,
Paseo del Bosque s/n, La Plata, B1900FWA, Bue nos Aire s, Argentina
pmc@fcaglp.unlp.edu.ar
C.M. GIORDANO
Grupo de Caos en Sistemas Hamiltonianos
Facultad de Ciencias Astron´omicas y Geof´ısicas, Instituto de Astrof´ısica de La Plata, Universidad
Nacional de La Plata, CONICET-CCT La Plata,
Paseo del B osque s/n, La Plata, B1900FWA, Bu enos Aires, Argentina
giordano@fcaglp.unlp.edu.ar
Received (to be inserted by publisher)
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 o f chaos in a general system is still lacking. Such a comparison could lead to select the
most efficient algorithms given a certain dynamical problem. Fur thermore, in order to choose the
appropriate numerical integrators to compute them, more compara tive studies among numerical
integrators are a lso needed.
This work deals with both problems. We first extend the work of [Maffione et al., 2 011a] for
mappings to the 2D [H´enon & Heiles, 1964] potential, and compare several variatio nal indicators
of chaos: the Lyapunov Indicato r (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
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