Theory and Applications of the Orthogonal Fast Lyapunov Indicator (OFLI and OFLI2) Methods

Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method

“…Although the computation of the mLCE is the most widely used technique for characterizing the regular or chaotic nature of orbits, its computational drawbacks, like for example its slow convergence to its limiting value, led to the development of a number of other, efficient chaos detection techniques, which make use of the solutions of the variational equations, like for example the fast Lyapunov indicator (FLI) and its variants [79,80,81,82,83,84], the mean exponential growth of nearby orbits (MEGNO) [85,86,87], the relative Lyapunov indicator (RLI) [88,89,90], the smaller alignment index (SALI) [91,92,93] and its generalization, the GALI [74,75,76,94].…”

Propagation of rays in 2D and 3D waveguides: a stability analysis with Lyapunov and Reversibility fast indicators

“…Finite time indicators such as the Fast Lyapunov Indicator (FLI) 16,17 have been first proposed to analyze the orbital stability. Other short term indicators of variational nature have been introduced: the Alignment Indices (SALI) 18 , the Orthogonal Fast Lyapunov Indicator (OFLI) 20 , the Mean Exponential Growth of Nearby Orbits (MEGNO) 21,22 , which is an excellent filter of the oscillations of FLI, the relative Lyapunov indicator (RLI) 23 , and the Generalized Lyapunov indicators (GALI), whose asymptotic behaviour is related the all the Lyapunov exponents 24,25 . An indicator based on the distribution of the stretching numbers (SSN) was also proposed 26,27 .…”

Stability study and dynamical analysis of the multicellular chopper

“…There have been many methods for detecting chaos from order. They include Poincaré sections, Lyapunov exponents (Skokos, 2017;Maffione et al, 2011), fast Lyapunov indicators (FLIs) (Lega et al, 2016;Barrio, 2016), smaller alignment index (SALI) and its generalised alignment index (Skokos and Manos, 2016), bifurcations, power spectra, frequency analysis, 0-1 test, geometrical criteria, and fractal basin boundaries, etc. Each of them has its advantages and drawbacks in classifying the attractors.…”

“…For a system of any dimension, the Lyapunov exponents, as a method of the average exponential deviation of two nearby orbits in the phase space, are efficient to distinguish regular from chaotic orbits, but quite a long integration times are often needed before obtaining reliable limit values. In addition, a more sensitive indicator, the FLI of Froeschlé (Lega et al, 2016;Barrio, 2016) is an ideal method. Distinction methods between chaotic and ordered orbits such as the small alignment index and fast Lyapunov indicator firstly used to discuss dissipative system in (Huang and Wu, 2012).…”