The inherent complexity in nonlinear business cycle model in resonance
作者： Junhai Ma , Tao Sun , Lixia Liu
DOI: 10.1016/J.CHAOS.2006.10.013
关键词: Bifurcation 、 Nonlinear system 、 Path (graph theory) 、 Applied mathematics 、 Mathematics 、 Chaotic 、 Dynamical systems theory 、 Phase (waves) 、 Amplitude 、 Annulus (firestop) 、 Control theory 、 General Mathematics
摘要: Abstract Based on Abraham C.-L. Chian’s research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions one category of business cycle model in resonance condition. We have also analyzed relation between amplitude phase as well outer excitements’ amplitude, frequency solutions, bifurcation parameters. Then studied quasi-periodical annulus periodical path leading chaotic state with different parameter combinations. Finally, conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation detecting complexity cycles systems future.
harvard.edu
elsevier.com
sci-hub.se 参考文章(7)
Ma Junhai, Chen Yushu, Liu Zengrong, THE MATRIC ALGORITHM OF LYAPUNOV EXPONENT FOR THE EXPERIMENTAL DATA OBTAINED IN DYNAMIC ANALYSIS Applied Mathematics and Mechanics-english Edition. ,vol. 20, pp. 985- 993 ,(1999) , 10.1007/BF02459061
Abraham C.-L. Chian, Felix A. Borotto, Erico L. Rempel, Colin Rogers, Attractor merging crisis in chaotic business cycles Chaos, Solitons & Fractals. ,vol. 24, pp. 869- 875 ,(2005) , 10.1016/J.CHAOS.2004.09.080
Ma Jun-hai, Chen Yu-shu, Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system(II) Applied Mathematics and Mechanics. ,vol. 22, pp. 1375- 1382 ,(2001) , 10.1007/BF02435540
Marek Szydłowski, Adam Krawiec, Janusz Toboła, Nonlinear oscillations in business cycle model with time lags☆ Chaos, Solitons & Fractals. ,vol. 12, pp. 505- 517 ,(2001) , 10.1016/S0960-0779(99)00207-6
Jun-hai Ma, Yu-shu Chen, Study on the prediction method of low-dimension time series that arise from the intrinsic nonlinear dynamics Applied Mathematics and Mechanics-english Edition. ,vol. 22, pp. 501- 509 ,(2001) , 10.1023/A:1016314129255
Tönu Puu, Irina Sushko, A Business Cycle Model with Cubic Nonlinearity Chaos Solitons & Fractals. ,vol. 19, pp. 597- 612 ,(2004) , 10.1016/S0960-0779(03)00132-2
Chen, Jun-hai(马军海), Ma, Yu-shu(陈予恕), STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(II) 应用数学和力学：英文版. pp. 1240- 1251 ,(2001)