In this paper , we obtain constrain qualifications of multi-object optimal programming with the Hadamard directional derivative , extend Maeda and Preda \'s results to some extent .

利用Hadamard方向导数这一工具，获得了不等式约束条件下多目标规划问题的约束品性，这一约束品性在某种程度上是Maeda和Preda等人研究结果的进一步推广.

The simulation results show that the strength of periodic restrictions and the strength and frequency of feeding on prey species have significant influences on the dynamical behaviors of preda - tor - prey systems . When the feeding rate is constant , the system goes from stable states through periodic ( anti - periodic ) fluctuations to extinction as the strength of periodic restriction increases .

结果表明周期激励强度、食饵常数存放率的大小、食饵周期存放以及周期存放的频度对系统行为都有很大的影响，当食饵存放率为零时，系统随周期激励强度的增大经历了稳定、周期波动、准周期波动和灭绝四种状态；