带有分段常数变量的Lorenz系统的稳定性和分支  

The Stability and Bifurcation Behavior of Lorenz System 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,陕西西安710062

出　　处：《应用数学》2014年第4期805-811,共7页Mathematica Applicata

基　　金：国家自然科学基金(60671063;11171199);中央高校基本科研业务费专项资金资助(GK201302006)

摘　　要：本文研究一类带有分段常数变量的Lorenz系统的稳定性和分支行为.首先通过计算转化得到Lorenz系统对应的差分系统,利用线性稳定性理论讨论平衡点局部渐近稳定的充要条件.其次选择差分系统三个参数的一个参数为分支参数,利用分支理论研究平衡点处产生Neimark-Sacker分支不变闭曲线的充要条件,并使用分支理论给出判断分支不变闭曲线的稳定性的阈值.最后数值模拟验证了理论分析的正确性.The stability and bifurcation behavior of a Lorenz system with piecewise constant arguments are investigated in present work.The discrete model determined the dynamical behavior of corresponding differential model is achieved by calculation.Firstly,the necessary and sufficient conditions for the local asymptotic stability of steady state are achieved on the linearized stability analyses.Secondly,by choosing aparameter of the discrete model as the bifurcation parameter and using the bifurcation theory,it is found that the discrete model undergoes a N-S bifurcation at an exceptive value of the parameter.Finally,numerical examples carry out to justify the main results in this work.

关 键 词：LORENZ系统 分段常数变量 稳定性 分支 

分 类 号：O175.1[理学—数学]