Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal conditions for the numerical calculation of the largest Lyapunov
  exponent for systems of ordinary differential equations   A general indicator of the presence of chaos in a dynamical system is the
largest Lyapunov exponent. This quantity provides a measure of the mean
exponential rate of divergence of nearby orbits. In this paper, we show that
the so-called two-particle method introduced by Benettin et al. could lead to
spurious estimations of the largest Lyapunov exponent. As a comparator method,
the maximum Lyapunov exponent is computed from the solution of the variational
equations of the system. We show that the incorrect estimation of the largest
Lyapunov exponent is based on the setting of the renormalization time and the
initial distance between trajectories. Unlike previously published works, we
here present three criteria that could help to determine correctly these
parameters so that the maximum Lyapunov exponent is close to the expected
value. The results have been tested with four well known dynamical systems:
Ueda, Duffing, R\"ossler and Lorenz.

15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph