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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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:912374
    DOI: 10.1155/2013/912374
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    References listed on IDEAS

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    1. Wang, Qiubao & Li, Dongsong & Liu, M.Z., 2009. "Numerical Hopf bifurcation of Runge–Kutta methods for a class of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3087-3099.
    2. Ding, Xiaohua & Su, Huan & Liu, Mingzhu, 2008. "Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 795-807.
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