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一类基因调控网络模型的Bogdanov-Takens分岔分析

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一类基因调控网络模型的Bogdanov-Takens分岔分析 曹建智, 谭军, 王培光河北大学数学与信息科学学院, 保定 071002 Bogdanov-Takens Bifurcation Analysis of a Gene Regulatory Network Model with Two Delays CAO Jianzhi, TAN Jun, WANG PeiguangCollege of Mathematics and Information Science, Hebei University, Baoding 071002, China
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摘要本文研究了一类具有双时滞的基因调控网络模型的动力学行为.首先,讨论了系统正平衡点的存在情况,并给出正平衡点处发生B-T分岔的条件.其次,利用普适开折,正规形和中心流形等相关理论,将靠近正平衡点的动力学行为转化为研究限制在中心流形上正规形的动力学特征.最后,对所得结果进行了数值模拟,给出靠近B-T分岔点的分岔曲线,得到相应的分岔图.并对所得结论进行了总结.
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收稿日期: 2019-05-07
PACS:34K17
34K18
34E10
基金资助:国家自然科学基金(11771115,11801128),河北省自然科学基金(A2018201109,A2019201396),河北大学工商学院第五批教改项目(JX201819)资助.

引用本文:
曹建智, 谭军, 王培光. 一类基因调控网络模型的Bogdanov-Takens分岔分析[J]. 应用数学学报, 2021, 44(2): 279-293. CAO Jianzhi, TAN Jun, WANG Peiguang. Bogdanov-Takens Bifurcation Analysis of a Gene Regulatory Network Model with Two Delays. Acta Mathematicae Applicatae Sinica, 2021, 44(2): 279-293.
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