摘要
研究了一类具有离散时滞和干扰项的广义造血模型的稳定性及Hopf分支.首先利用函数的单调性,证明了模型正平衡态的存在唯一性;然后利用分支理论及周期函数正交性等方法给出了模型Hopf分支存在的充分条件,并得到了分支周期解的近似解析表达式和判断周期稳定性的计算公式;最后通过实例验证了理论分析和数值计算的一致性,并运用Matlab绘制了造血模型数值解的拟合图.
The stability and approximate expression of Hopf bifurcation periodic solution arediscussed for a class of general hematopoiesis model with time delay and interference.First of all,The necessary and sufficient conditions of the existence and uniquity of the positive equlibria by applying functional derivative is obtained;After that,the form of approximate periodic solution is derived by the orthogonal method;In the end,the achievability of the results is verified by examples.The fitted curves are achieved by Matlab when assign the different parmaters to the model.
出处
《云南师范大学学报（自然科学版）》
2010年第6期34-38,57,共6页
Journal of Yunnan Normal University:Natural Sciences Edition
基金
国家自然科学基金资助项目(10871122)
国家自然科学基金资助项目(60671063)
关键词
广义造血模型
周期解
时滞
HOPF分支
General hematopoiesis model
Periodic solution
Delay
Hopf bifurcation
