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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 316390, 18 pages
http://dx.doi.org/10.1155/2012/316390
Research Article

Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos

Department of Electronic Information Engineering, Huanghe Science and Technology College, Henan, Zhengzhou 450063, China

Received 14 October 2011; Revised 15 January 2012; Accepted 23 January 2012

Academic Editor: Chuanhou Gao

Copyright © 2012 Rongyan Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A kind of nonlinear finance system with time-delayed feedback is considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associate characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the stability, direction, and other properties of bifurcating periodic solutions. Finally, we give several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a stable periodic orbit.