Journal of Applied Mathematics
Volume 2013 (2013), Article ID 912374, 11 pages
Research Article

Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback

1Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China
2School of Science, China University of Petroleum (East China), Qingdao 266555, China

Received 6 May 2013; Accepted 21 June 2013

Academic Editor: Junjie Wei

Copyright © 2013 Yuanyuan Wang and Xiaohua Ding. 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.


We consider a complex autonomously driven single limit cycle oscillator with delayed feedback. The original model is translated to a two-dimensional system. Through a nonstandard finite-difference (NSFD) scheme we study the dynamics of this resulting system. The stability of the equilibrium of the model is investigated by analyzing the characteristic equation. In the two-dimensional discrete model, we find that there are stability switches on the time delay and Hopf bifurcation when the delay passes a sequence of critical values. Finally, computer simulations are performed to illustrate the theoretical results. And the results show that NSFD scheme is better than the Euler method.