  A method is given for generating a bounded invariant of a differential system
with a given set of initial conditions around a point $x_0$. This invariant has
the form of a tube centered on the Euler approximate solution starting at
$x_0$, which has for radius an upper bound on the distance between the
approximate solution and the exact ones. The method consists in finding a real
$T>0$ such that the "snapshot" of the tube at time $t=(i+1)T$ is included in
the snapshot at $t=iT$, for some integer $i$. In the phase space, the invariant
is therefore in the shape of a torus. A simple additional condition is also
given to ensure that the solutions of the system can never converge to a point
of equilibrium. In dimension 2, this ensures that all solutions converge
towards a limit cycle. The method is extended in case the dynamic system
contains a parameter $p$, thus allowing the stability analysis of the system
for a range of values of $p$. This is illustrated on classical Van der Pol's
system.
