Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/912374 |
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| Summary: | 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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| ISSN: | 1110-757X 1687-0042 |