  Based on both qualitative method and numerical tests for a series of
particular cases in the parameter region, a=1, 0<b <1, it is shown that the
three-dimensional system (2) may have a series of interesting phenomena on the
non-trivial local attractors, such as the faint attractor (this term is
suggested by the author), the local attractor with complex structure, twin
spatial limit closed orbits, the bifurcation of rotation numbers, and the
spatial limit cycle, etc.. The system (2) is a very rich source in the study of
dynamical system theory.
