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

Abstract EN

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.