捕食者具有性别结构及时滞的母系社会捕食模型

Maternal society predator-prey model with time delay and sex structure to predator

研究了捕食者具有性别结构及时滞的母系社会捕食模型.通过计算雅克比矩阵的特征值得到了系统正平衡点局部稳定性的充分条件,当时滞τ穿过τ0时,系统在正平衡点附近产生Hopf分支及周期解.运用迭代法得出正平衡点全局渐近稳定的条件;运用隐函数存在定理,分析了捕食者的出生率对各个种群密度的影响,并研究了雌性捕食者死亡率对雌性捕食者幼崽出生率的影响.举例说明了所得结果的有效性.

A kind of predator-prey model in maternal society with time delay and sex structure to predator is investigated in this paper.By analyzing the eigenvalues of Jacobian matrices,the sufficient conditions of the local stability of the positive equilibrium are obtained,when the delayτcrosses some critical valueτ0,Hopf bifurcations and periodic solutions occur at the positive equilibrium of the system.Furthermore,by the iterative method,the conditions of global stability for the positive equilibrium are discussed.By the theorem of the existence of implicit function,the influence of the birth rates on densities of species is analyzed,moreover,the effect of the death rate of female predator with respect to the birth rate of female predator is investigated.Finally,numerical simulations are carried out to illustrate our main results.