四维金融模型的稳定性分析与时滞反馈  

Stability Analysis of Four-dimensional Finance Model and Time Delayed Feedback

作　　者：张二丽[1] 邢玉清 ZHANG Er-li;XING Yu-qing(School of Statistics and Big Data,Zhengzhou College of Finance and Economics,Zhengzhou,450044,China;School of Cybersecurity,Information Engineering University,Zhengzhou 450001,China;College of Sciences,Henan Agricultural University,Zhengzhou 450002,China)

机构地区：[1]郑州财经学院统计与大数据学院,河南郑州450044 [2]信息工程大学网络空间安全学院,河南郑州450001 [3]河南农业大学理学院,河南郑州450002

出　　处：《数学的实践与认识》2022年第10期37-44,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目(12161069);河南省高等学校重点科研项目(21A110023);河南省教科文卫体系统“劳模和工匠人才创新工作室”(豫教科文卫体工【2021】21号);宁夏自然科学基金项目(2022AAC05044);郑州财经学院学术技术带头人培养对象重点培育项目(郑财院发【2021】20号);河南农业大学创新基金(KJCX2017A19)。

摘　　要：首先以投资成本为分支参数,研究了模型平衡点的稳定性与Hopf分支的存在性.其次,在投资需求上增加时滞反馈项,使模型更符合实际.然后以时滞为分支参数,研究时滞对模型平衡点的稳定性和分支存在性的影响,研究发现当时滞经过一系列临界值时,模型的平衡点失稳,并且出现Hopf分支和Hopf-zero分支.最后,数值模拟验证了理论结果。Firstly,choosing investment cost as the bifurcation parameter,the stability of equilibrium point and the existence of Hopf bifurcation are studied.Secondly,in order to make the model more realistic,a time delayed feedback is added to the investment demand.Taking the delay as the bifurcation parameter,we consider the effect of delay on the stability of equilibrium point and the existence of bifurcation.It is found that the equilibrium point will lose its stability and the Hopf bifurcation and Hopf-zero bifurcation arise if the time delay passed a sequence of critical values.Finally,some numerical simulation are carried out to support the analytic results.

关 键 词：稳定性 HOPF分支 Hopf-zero分支 时滞反馈 

分 类 号：O175[理学—数学] F830[理学—基础数学]