中立型双时滞Logistic模型分支分析及人口预测  

Bifurcation analysis of the neutral logistic equation with double delays and population predictions

作　　者：梁璐莎 陈斯养[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《云南大学学报（自然科学版）》2015年第3期335-344,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(10871122;11171199)

摘　　要：讨论了中立型双时滞Logistic模型的稳定性及分支存在性.应用Jury判据得到正平衡态局部渐近稳定的充分条件;运用中心流形定理和分支理论并以种群的内禀增长率为分支参数,给出了模型Flip分支和N-S分支存在性条件与分支方向,简略给出了模型F-N-S分支存在的充要条件;利用中国1981—2010年人口数据得到模型中参数的拟合数值,验证了理论的正确性,并对未来人口控制方向提出建议.The principal objective is to discuss the stability and bifurcations of the neutral logistic equation.Some sufficient conditions for the local asymptotical stability of the equilibrium have been provided by employing Jury criterion.Further,the existences of Flip and N-S bifurcations are discussed by using center manifold theorem and bifurcation theory,and we briefly address the necessary and sufficient conditions for the existence of F-N-S bifurcation.By fitting the population data set of Chinese population from 1981 to 2010 we determine the parameter values,which allows us to evaluate the proposed model and discuss the control strategy for controlling the population in China.

关 键 词：中立型 稳定性 Flip分支 N-S分支 F-N-S分支 数值拟合 

分 类 号：O175.7[理学—数学]