带时滞的草-鼠模型

摘要

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.