向日葵方程的周期扰动Hopf分支  

Periodically Perturbed Hopf Bifurcation of Sunflower Equation

作　　者：殷红燕[1] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2010年第4期115-117,共3页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(60904005);湖北省自然科学基金资助项目(2009CDB026)

摘　　要：研究了向日葵方程在经历Hopf分支时,小周期扰动对系统的影响,特别是讨论了扰动频率与Hopf分支固有频率在调和共振的情形,表明了在某些参数区域内,系统存在调和解分支,并且证明了分支解的稳定性.In this paper the influence of small periodic perturbations on Sunflower equation exhibiting Hopf bifurcation is studied . In particular, the excitation frequency and the critical natural frequency of Hopf bifurcation in the case of harmonic resonance are discussed. It is shown that in some parameter regions the systems exhibit harmonic solution bifurcation . Furthermore, the stability of bifurcation periodic solutions is discussed.

关 键 词：向日葵方程 HOPF分支 调和解 稳定性 

分 类 号：O175[理学—数学]