带有分段常数变量的单种群模型的稳定性和分支行为（英文）  

Stability and Bifurcation Analysis of a Population Model with Piecewise Constant Arguments

作　　者：王烈[1] 陈斯养[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2014年第1期125-138,共14页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(60671063;11171199);the Fundamental Research Funds of the Central Universities(GK201302006)

摘　　要：本文研究了带有分段常数变量的单种群连续模型的稳定性和分支行为.首先,通过计算将连续模型转化为对应的差分模型,使用线性稳定性理论在三种情况下研究了差分模型在正平衡态处局部渐近稳定的充分条件.其次,将参数r作为分支参数,利用分支理论研究了差分模型在正平衡态处产生翻转分支的条件.最后,数值模拟验证了理论分析的正确性.The stability and bifurcation behavior of a population model with piecewise con-stant arguments are investigated in this paper. The discrete model determining the dynamical behavior of corresponding differential model is achieved by calculation. Firstly, the sufficient conditions for the local asymptotic stability of the steady state are achieved in three aspects based on the linearized stability analysis. Secondly, by choosing the parameter r as the bifurcation parameter and using the bifurcation theory, we find that the discrete equation undergoes a flip bifurcation at an excep-tive value of the parameter r. Finally, numerical examples are carried out to justify the main results in this work.

关 键 词：差分方程 分段常数变量 稳定性 翻转分支 

分 类 号：O175.7[理学—数学]