  A phenomenon of weak transient chaos is discussed that is caused by
sub-exponential divergence of trajectories in the basin of a non-chaotic
attractor. Such a regime is not easy to detect, because conventional
characteristics, such as the largest Lyapunov exponent is non-positive. Here we
study, how such a divergence can be exposed and detected. First, we show that
weak transient chaos can be exposed if a small random perturbation is added to
the system, leading to positive values of the largest Lyapunov exponent.
Second, we introduce an alternative definition of the Lyapunov exponent, which
allows us to detect weak transient chaos in the deterministic unperturbed
system. We show that this novel characteristic becomes positive, reflecting
transient chaos. We demonstrate this phenomenon and its detection using a
master-slave system where the master possesses a heteroclinic cycle attractor,
while the slave is the Van-der-Pol-Duffing oscillator possessing a stable limit
cycle.
