  This work presents the continuation of the recent article "The Lorenz system:
hidden boundary of practical stability and the Lyapunov dimension", published
in the Nonlinear Dynamics journal. In this work, in comparison with the results
for classical real-valued Lorenz system (henceforward -- Lorenz system), the
problem of analytical and numerical identification of the boundary of global
stability for the complex-valued Lorenz system (henceforward -- complex Lorenz
system) is studied. As in the case of the Lorenz system, to estimate the inner
boundary of global stability the possibility of using the mathematical
apparatus of Lyapunov functions (namely, the Barbashin-Krasovskii and LaSalle
theorems) is demonstrated. For additional analysis of homoclinic bifurcations
in complex Lorenz system a special analytical approach by Vladimirov is
utilized. To outline the outer boundary of global stability and identify the
so-called hidden boundary of global stability, possible birth of hidden
attractors and transient chaotic sets is analyzed.
