纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
3期
240-244
,共5页
Hopf分支%平均法%调和解分支%次调和解分支%稳定性
Hopf分支%平均法%調和解分支%次調和解分支%穩定性
Hopf분지%평균법%조화해분지%차조화해분지%은정성
Hopf bifurcation%method of averaging%harmonic solution bifurcation%subharmonic solution bifurcation%stability
研究了小周期扰动对一类存在Hopf 分支的非线性系统的影响。特别是应用平均法讨论了扰动频率与Hopf分支固有频率在共振及二阶次调和共振的情形周期解分支的存在性。表明了在某些参数区域内，系统存在调和解分支和次调和解分支，并进一步讨论了二阶次调和分支周期解的稳定性。
研究瞭小週期擾動對一類存在Hopf 分支的非線性繫統的影響。特彆是應用平均法討論瞭擾動頻率與Hopf分支固有頻率在共振及二階次調和共振的情形週期解分支的存在性。錶明瞭在某些參數區域內，繫統存在調和解分支和次調和解分支，併進一步討論瞭二階次調和分支週期解的穩定性。
연구료소주기우동대일류존재Hopf 분지적비선성계통적영향。특별시응용평균법토론료우동빈솔여Hopf분지고유빈솔재공진급이계차조화공진적정형주기해분지적존재성。표명료재모사삼수구역내，계통존재조화해분지화차조화해분지，병진일보토론료이계차조화분지주기해적은정성。
The influence of small periodic perturbations on a kind of nonlinear systems exhibiting Hopf bi-furcation is studied. In particular, we discuss the existence of bifurcating periodic solutions in the case that the excitation frequency and the critical natural frequency of Hopf bifurcation is resonance and subharmonic resonance. In this work, the ideas related method of averaging. It is shown that in some parameter regions the systems exhibit harmonic solution bifurcation and subharmonic solution bifurcation. Furthermore, the stability of subharmonic solutions is discussed.
