H-1}}\sec h\frac{\omega \pi }{2\sqrt{\Lambda H-1}}=0.$$ The above necessary condition is irrelative to the time-independent trap asymmetry $\Delta E_{0}$, this means the chaotic oscillations are caused by the time-dependent trap asymmetry, but it is not to say that the stability is irrelative to the time-independent trap asymmetry, actually, the sufficient-necessary conditions and high-order necessary conditions are relations of it and other parameters. For the same parameters, the distribution of stability curves sensitive depends on the initial conditions, to show explicitly this dependence we have chosen a series of value of the initial constant $C_{0}$, with the growing of the value of $%
C_{0}$, the curves become denser and denser, this illustrates the existence of chaos, see Fig. 2. The changing between the regular oscillations and the chaotic oscillations is showed in Fig.3. Regions above the curves correspond to chaotic oscillations of the fractional population imbalance and those below correspond to regular oscillations. There exist two chaotic regions separated by a special frequency which is determined by the physical parameters, and this frequency can cause an unstable nonlinear resonance. When the damping becomes stronger and stronger, the regions of chaotic oscillations become smaller and smaller, and the regular region becomes larger and 