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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) schemewe study the dynamics of this resulting system. The stability of the equilibrium of the model is investigatedby analyzing the characteristic equation. In the two-dimensional discrete model, we find that there are stability switches on thetime delay and Hopf bifurcation when the delay passes a sequence of criticalvalues. Finally, computer simulations are performed to illustrate thetheoretical results. And the results show that NSFD scheme is better than the Euler method

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