Dynamics of a nonstandard finite-difference scheme for a limit cycle oscillator with delayed feedback

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. © 2013 yuanyuan wang and xiaohua ding.