研究了捕食者与食饵均具有线性密度制约的Ivlev型捕食模型的平衡态问题,寻找两种群能够共存的条件.利用线性算子的特征值理论、扰动理论和分歧理论,以扩散系数为分歧参数,证明了在一定条件下系统在正常数平衡态附近存在分歧现象,且局部分支可以延拓成整体分支,同时还给出了分歧点附近解的结构.结果显示,捕食者(天敌)的扩散系数选取适当时两种群可以并存.%The steady-state problem of the Ivlev's type predator-prey systems with prey and predator both having linear density restricts is studied. The conditions for the two populations' coexistence are looked for. Using eigenvalue theory, perturbation theory and bifurcation theory of linear operator, the bifurcation from constant steady-state solution in a certain condition is obtained, when diffusion coefficient as bifurcation parameter is used. Moreover, the local branch could extend to global branch and the structure near bifurcation point is given. Two populations can coexist with appropriate diffusion coefficient of predator (natural enemy).
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