中文摘要：

考虑到种群个体存在生长延缓的情况,建立了一类资源量与种群规模共同演化的离散尺度结构模型.首先分析模型零解的稳定性,通过对雅可比矩阵特征值的分析得到零解渐近稳定的条件.当零解不稳定时,分析非零平衡解的存在性,同时得到种群能存活所应满足的必要条件.最后利用数值分析法,借助分支图揭示了参数变化对种群规模的影响.通过模拟分析发现,为了使种群稳定,生长延缓可以降低对繁殖率的要求,因此个体的生长延缓有助于维持种群的稳定性.

英文摘要：

With an observation of individuals slowly growth,a kind of discrete size-structured population model with resources-dependence is established.Firstly,we analyze the stability of the zero solution of the model,and derived some conditions under which the zero solution is asymptotically stable via the analysis of the characteristic value of the Jacobian.Next,when the zero solution became unstable,we discuss the existence of the non-zero steady state and the conditions for the survival of the population.At last,by numerical methods,the influence of the parameters variation on the population size is revealed by the bifurcation diagrams.Through the simulation analysis,in order to maintain the stability of population equilibrium,growth retardation may relax the requirements of fertility,which means that growth retardation is helpful to keep the population stability.