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研究一类具有鼠类作用的三维非线性红松林种群的数学模型；并利用三维的Ｈｏｐｆ分支定理得到了对充分小的δ＜０时，存在不稳定的周期解．
The mathematical model of a three-dimensional nonlinear Pinus koraiensis forest population with rodents was studied. By using the Hopf bifurcation theorem of three-dimensional, we found that for a sufficiently small δ <0, there exists an unstable periodic solution.