时滞广告量-购物水平模型稳定性和Hopf分支研究

Study on Hopf bifurcation and stability for advertising-shopping level model with delay

讨论了具有时滞的广告量-购物水平模型的稳定性和Hopf分支.应用Hopf分支理论和泛函微分方程方法研究了该模型的线性稳定性和局部Hopf分支.把时滞变量当做分支参数,利用规范型理论和中心流形定理给出了确定分支方向及分支周期解稳定性的计算公式,且通过数值模拟验证结论的有效性.

The model of Hopf bifurcation of advertising-shopping and stability with time delay was studied. By applying of the theory of hopf bifurcation and functional differential equation method, this paper discussed the linear stability of the model and the local Hopf bifurcation. The time delay was considered as a bifurcation parameter. By using the normal form theory and center manifold methods, the calculation formula was obtained for determining direction of Hopf bifurcations and bifurcating periodic solution stability. The numerical simulation showed the effectiveness of the conclusion.