Variational calculation of the limit cycle and its frequency in a two-neuron model with delay.

@article{Brandt2006VariationalCO,
  title={Variational calculation of the limit cycle and its frequency in a two-neuron model with delay.},
  author={Sebastian F. Brandt and Axel Pelster and Ralf Wessel},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2006},
  volume={74 3 Pt 2},
  pages={036201}
}
We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle emerges via a supercritical Hopf bifurcation. First, we calculate its frequency and trajectory perturbatively by applying the Poincaré-Lindstedt method. Then, the perturbation series are resummed by means of the Shohat expansion in good agreement with numerical… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 22 references

Physica D 130

  • J. Wei, S. Ruan
  • 255
  • 1999
Highly Influential
5 Excerpts

Dynamics of Small Neural Populations

  • J. Milton
  • (Amer. Math. Soc., Providence,
  • 1996
Highly Influential
3 Excerpts

Eur

  • J. Dreger, A. Pelster, B. Hamprecht
  • Phys. J. B 45, 355
  • 2005
3 Excerpts

Rev

  • J. Bechhoefer
  • Mod. Phys. 77, 783
  • 2005
2 Excerpts

Neural Networks 17

  • X. Liao, S. Li, G. Chen
  • 545
  • 2004
2 Excerpts

Physica D 191

  • S. Ruan, R. S. Filfil
  • 323
  • 2004
2 Excerpts

Nonlinear Dynam

  • X. Liao, S. Li, K.-W. Wong
  • 31, 299
  • 2003
2 Excerpts

A

  • H. Kleinert
  • Pelster, and M.V. Putz: Phys. Rev. E 65, 066128
  • 2002
3 Excerpts

Bio

  • C. W. Eurich, M. C. Mackey, H. Schwegler, J. Theor
  • 216, 31
  • 2002
2 Excerpts

Introduction to Neural Dnamics and Signal Transmission

  • J. Wu
  • Delay (Walter de Gruyter, Berlin,
  • 2001
2 Excerpts

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