【摘要】 应用Liapunov-Schmidt约化方法,研究了一类滞时微分方程的Hopf分歧问题,在Hopf分歧点的附近,给出了周期解枝的近似解析表达式,同时用Liapunov-Schmidt约化方法结合分片Hermite插值多项式的配王法求解了Hopf分歧点附近的周期解枝,发现理论分析结果和数值结果吻合,证实了用Liapunov-Schmidt约化方法求解滞时微分方程周期解的有效性与可行性．更多还原

【Abstract】 Using the Liapunov-Schmidt reduction,we investigate the Hopf bifurcation of a class of delayed differential equations. Near the Hopf bifurcation point, we obtain the periodic solution branch bifurcated from the trivial solution. An approximate analytic expression of the periodic solution is given to compare with the numerical results, which are computed by the collocation method based on piesewise Hermite polynomials. The fact that the approximate analytic periodic solution nearly coincides with the numerical results shows the effectiveness of our analysis.更多还原