The complexity of an investment competition dynamical model with imperfect information in a security market

被引:23
作者
Xin, Baogui [1 ,2 ]
Ma, Junhai [2 ]
Gao, Qin [2 ]
机构
[1] Shandong Univ Sci & Technol, Sch Econ & Management, Qingdao 266510, Peoples R China
[2] Tianjin Univ, Nonlinear Dynam & Choos Group, Sch Management, Tianjin 300072, Peoples R China
基金
中国国家自然科学基金;
关键词
COURNOT GAME; BOUNDED RATIONALITY; DUOPOLY GAME; MULTISTABILITY; STABILITY; SYSTEMS; CHAOS;
D O I
10.1016/j.chaos.2009.03.110
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We present a nonlinear discrete dynamical model of investment competition with imperfect information for N heterogeneous oligopolists in a security market. In this paper, our focus is on a given three-dimensional model which exhibits highly rich dynamical behaviors. Based on Wen's Hopf bifurcation criterion [Wen GL. Criterion to identify Hopf bifurcations in maps of arbitrary dimension. Phys Rev E 2005:72:026201-3; Wen GL, Xu DL, Han X. On creation of Hopf bifurcations in discrete-time nonlinear systems. Chaos 2002;12(2):350-5] and Kuznetsov's normal form theory [Kuznetsov YA. Elements of applied bifurcation theory. New York: Springer-Verlag; 1998. p. 125-37], we study the model's stability, criterion and direction of Neimark-Sacker bifurcation. Moreover, we numerically simulate a complexity evolution route: fixed point, closed invariant curve, double closed invariant Curves, fourfold closed invariant curves, strange attractor, period-3 closed invariant curve, period-3 2-tours, period-4 closed invariant curve, period-4 2-tours. (c) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2425 / 2438
页数:14
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