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.