  Stable chaos refers to the long irregular transients, with a negative largest
Lyapunov exponent, which is usually observed in certain high-dimensional
dynamical systems. The mechanism underlying this phenomenon has not been well
studied so far. In this paper, we investigate the dynamical formation of stable
irregular transients in coupled discontinuous map systems. Interestingly, it is
found that the transient dynamics has a hidden pattern in the phase space: it
repeatedly approaches a basin boundary and then jumps from the bundary to a
remote region in the phase space. This pattern can be clearly visualized by
measuring the distance sequences between the trajectory and the basin boundary.
The dynamical formation of stable chaos originates from the intersection points
of the discontinuous boundaries and their images. We carry out numerical
experiments to verify this mechanism.
