具分段常数变量及干扰的反馈控制模型的N-S分支  

The N-S Bifurcation of Feedback Control Model with Piecewise Constant Arguments and Interference

作　　者：陈斯养[1] 靳宝[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》2015年第1期85-97,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10871122;11171199);中央高校基本科研业务费专项资金(GK201302004;GK201302006)~~

摘　　要：本文讨论了具有分段常数变量及干扰的单种群反馈控制模型的稳定性及N-S分支等问题.通过计算得到微分模型对应的差分模型,基于特征值理论和Schur-Cohn判据得到正平衡态局部渐进稳定的充分条件,以种群的内禀增长率为分支参数,运用分支理论和中心流形定理分析了Neimark-Sacker分支的存在条件;通过数值模拟验证理论的正确性.结果表明,当单种群反馈控制模型增加分段常数变量及干扰后,模型将会变得非常复杂;平衡态稳定性的开关现象会随着种群数量对于内禀增长率的影响而发生变化,随之将会产生Neimark–Sacker分支现象.The dynamics of the feedback control model on a single population with piecewise constant arguments and interference are investigated in this paper. A difference model which can equi-valently describe the dynamical behavior of the original differential model is deduced. Based on the analysis of the eigenvalues and Schur-Cohn criterion, the su？cient conditions for local asymptotic stability of the positive equilibrium are achieved. Moreover, by choosing the intrinsic growth rate of the population as the bifurcation parameter and applying the bifurcation and center manifold theories, the existence conditions for the Neimark-Sacker bifurcation of this difference model is derived. Finally, some numerical examples substantiating our theoretical predictions are given and the numerical simulations also show that： 1） the dynamics of the single population of feedback control model are very complex when we consider piecewise constant arguments and interference; and 2） the positive equilibrium of the model switches from stable to unstable as the intrinsic growth rate of population increases beyond a critical value, at which the unique supercritical Neimark-Sacker bifurcation will occur.

关 键 词：分段常数变量 反馈控制 干扰 N-S分支 

分 类 号：O175.7[理学—数学]