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2013 Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback
Yuanyuan Wang, Xiaohua Ding
J. Appl. Math. 2013: 1-11 (2013). DOI: 10.1155/2013/912374

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.

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Yuanyuan Wang. Xiaohua Ding. "Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/912374

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1271.65116
MathSciNet: MR3082124
Digital Object Identifier: 10.1155/2013/912374

Rights: Copyright © 2013 Hindawi

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