中文摘要：

基于尖点突变的性质,对修改后的Logistic模型进行变换,并将其化为具有尖点突变的标准模型.利用微分方程定性理论,对模型进行分析,并根据突变理论,给出突变发生的条件.最后利用仿真验证结论的正确性.

英文摘要：

Based on the properties of cusp catastrophe, the modified Logistic model is trans- formed to the standard form with cusp catastrophe. The model is analyzed using the qual- itative theory of differential equations and the conditions of catastrophe are given by the catastrophe theory. Finally, the simulations are carried to prove the results.