In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large s...In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.展开更多
本文对Borisuk M T和Tyson J J在[1]中所提出的一个有关蛙卵有丝分裂的平面三次系统模型证明了鞍结点不变圈的存在性,给出了鞍结点不变圈所在的空间区域和所对应的参数区域.所得结果严格地证明了[1]中给出的数值结果.此外,我们还给出了...本文对Borisuk M T和Tyson J J在[1]中所提出的一个有关蛙卵有丝分裂的平面三次系统模型证明了鞍结点不变圈的存在性,给出了鞍结点不变圈所在的空间区域和所对应的参数区域.所得结果严格地证明了[1]中给出的数值结果.此外,我们还给出了从此鞍结点不变圈分支出极限环的条件.展开更多
基金the the National Natural Science Foundation of China (No.10171099).
文摘In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.
