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

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  • Yuanyuan Wang
  • Xiaohua Ding

Abstract

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.

Suggested Citation

  • Yuanyuan Wang & Xiaohua Ding, 2013. "Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, July.
    • Handle: RePEc:hin:jnljam:912374
    DOI: 10.1155/2013/912374
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