  We perform a dynamical analysis of the recently published radial velocity
(RV) measurements of a few solar type stars which host multiple Jupiter-like
planets. In particular, we re-analyze the data for HD 202206, 14 Her, HD 37124
and HD 108874. We derive dynamically stable configurations which reproduce the
observed RV signals using our method called GAMP (an acronym of the Genetic
Algorithm with MEGNO Penalty). The GAMP relies on the N-body dynamics and makes
use of genetic algorithms merged with a stability criterion. For this purpose,
we use the maximal Lyapunov exponent computed with the dynamical fast indicator
MEGNO. Through a dynamical analysis of the phase-space in a neighborhood of the
obtained best-fit solutions, we derive meaningful limits on the parameters of
the planets. We demonstrate that GAMP is especially well suited for the
analysis of the RV data which only partially cover the longest orbital period
and/or correspond to multi-planet configurations involved in low-order mean
motion resonances (MMRs). In particular, our analysis reveals a presence of a
second Jupiter-like planet in the 14 Her system (14 Her c) involved in a 3:1 or
6:1 MMR with the known companion b. We also show that the dynamics of the HD
202206 system may be qualitatively different when coplanar and
mutually-inclined orbits of the companions are considered. We demonstrate that
the two outer planets in the HD 37124 system may reside in a close neighborhood
of the 5:2 MMR. Finally, we found a clear indication that the HD 108874 system
may be very close to, or locked in an exact 4:1 MMR.
