一个描述昆虫的数学模型的定性分析

The Qualitative Analysis of a Model on Insects

研究控制有害昆虫时提出的数学模型dN/DT=N(aN/N+n-b)g-kN(N+n),dn/dt=rN-bn,证明了该系统在条件b<ra-r/a+r下存在周期解,因此有害昆虫不会得到根除。如果以常数速率δ投放不育昆虫则在一定条件下有害昆虫书被根除。

A differential equation model on insects dN/dt=N(dN/N+n-b)- n), dn/dt=δ + rN-bn is discussed. It proves that if b<ra-r/a+r holds,then there is a periodic orbit and so the population N will not be eradicated. If one fosters a number of sterile insects in the population as a constant ratio δ, then under some condition, the population N will be eradicated.