带时滞的草—鼠模型

A Grass-rodent Model with Delay

建立了一类带有时滞的草-鼠模型,利用特征方程、Hurwitz判据和Bendixson-Dulac定理等,研究了该模型平衡点的存在性及稳定性,并给出了一列Hopf分支值,其次利用中心流行定理和正规型方法,给出确定分支周期性及分支方向的结论。

A grass - rodent model with time delay was established. The existence and stability of the equi- libriums were investigated by using the characteristic equations, Hurwitz criterion, Bendixson - Dulac theorem etc. , and a list values of Hopf bifurcation was given. By using the center manifold theorem and normal form method, the conclusions which determined the periodicity and direction of bifurcation were obtained.