统计与决策2024，Vol.40Issue(9)：67-72,6.DOI:10.13546/j.cnki.tjyjc.2024.09.011
一类非线性金融系统的多尺度效应研究
Study on the Multi-scale Effects of a Kind of Nonlinear Financial System
摘要
Abstract
Based on a kind of classical nonlinear financial system,and considering the perturbation with slow variable param-eter,this paper finds that there are strange non-chaotic bursting oscillation and chaotic bursting oscillation in the operation of the financial system.The bifurcation theory and slow-fast analysis method are used,and the dynamic mechanism of the behavior that autonomous system regulates slow-fast non-autonomous system is given.The BP-type strange non-chaotic bursting oscillation is related to the pitchfork bifurcation and stable focus attractor of the autonomous system.At the same time,the singularity of the non-autonomous system oscillation is due to the symmetric focus attractors generated by the pitchfork bifurcation of the autono-mous system,which leads to the"randomness"of the one-way access to the symmetric attractor of the non-autonomous system,that is,the two motion modes of up and up,down and down will appear randomly.As the parameter changes,the BP-HP chaotic bursting oscillation appears,which is closely related to the pitchfork bifurcation,Hopf bifurcation,stable focus and stable limit cy-cle attractor of the autonomous system,while the non-autonomous system has"randomness"in both directions of access to the symmetric attractor,that is,up and up,down and down,up and down,down and up,the four motion patterns will appear randomly,causing the evolution of strange non-chaotic bursting to evolve into chaotic bursting.Finally,the influence law of the perturbation amplitude of unit investment cost on bifurcation and cluster oscillation is presented.关键词
金融系统/簇发/分岔/混沌/奇异非混沌Key words
financial system/bursting/bifurcation/chaos/strange non-chaos分类
管理科学引用本文复制引用
刘玲玉,李向红,王宏斌..一类非线性金融系统的多尺度效应研究[J].统计与决策,2024,40(9):67-72,6.基金项目
国家自然科学基金资助项目(12172233 （）
U1934201 （）
11672191) （）
