Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 405639, 12 pages
doi:10.1155/2010/405639
Research Article

Neimark-Sacker Bifurcation in a Discrete-Time Financial System

Baogui Xin,1,2 Tong Chen,1 and Junhai Ma1

1Nonlinear Dynamics and Chaos Group, School of Management, Tianjin University, Tianjin 300072, China
2Center for Applied Mathematics, School of Economics and Management, Shandong University of Science and Technology, Qingdao 266510, China

Received 14 May 2010; Revised 16 July 2010; Accepted 28 August 2010

Academic Editor: Akio Matsumoto

Copyright © 2010 Baogui Xin et al. 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 discrete-time financial system is proposed by using forward Euler scheme. Based on explicit Neimark-Sacker bifurcation (also called Hopf bifurcation for map) criterion, normal form method and center manifold theory, the system's existence, stability and direction of Neimark-Sacker bifurcation are studied. Numerical simulations are employed to validate the main results of this work. Some comparison of bifurcation between the discrete-time financial system and its continuous-time system is given.