Weakly Connected Quasi-periodic Oscillators, FM Interactions, and Multiplexing in the Brain

@article{Izhikevich1999WeaklyCQ,
  title={Weakly Connected Quasi-periodic Oscillators, FM Interactions, and Multiplexing in the Brain},
  author={Eugene M. Izhikevich},
  journal={SIAM Journal of Applied Mathematics},
  year={1999},
  volume={59},
  pages={2193-2223}
}
We prove that weakly connected networks of quasi-periodic (multifrequency) oscillators can be transformed into a phase model by a continuous change of variables. The phase model has the same form as the one for periodic oscillators with the exception that each phase variable is a vector. When the oscillators have mutually nonresonant frequency (rotation) vectors, the phase model uncouples. This implies that such oscillators do not interact even though there might be physical connections between… CONTINUE READING
28 Extracted Citations
50 Extracted References
Similar Papers

Citing Papers

Publications influenced by this paper.
Showing 1-10 of 28 extracted citations

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 50 references

Weakly Connected Neural Networks

  • F. C. Hoppensteadt, E. M. Izhikevich
  • Springer- Verlag, New York
  • 1997
Highly Influential
15 Excerpts

n:m phase-locking of weakly coupled oscillators

  • G. B. Ermentrout
  • J. Math. Biol., 12
  • 1981
Highly Influential
5 Excerpts

Differential Topology

  • M. W. Hirsch
  • Springer-Verlag, New York
  • 1976
Highly Influential
4 Excerpts

Neural Organization

  • M. A. Arbib, P. Érdi, J. Szentágothai
  • MIT Press, Cambridge, MA
  • 1998
1 Excerpt

Three coupled oscillators : Mode - locking , global bifurcations and toroidal chaos

  • S. Kim, R. S. MacKay
  • 1998

Quasi-Periodic Motions in Families of Dynamical Systems

  • H. W. Broer, G. B. Huitema, M. B. Sevryuk
  • Springer-Verlag, Berlin, Heidelberg
  • 1996
1 Excerpt

Chains of coupled oscillators

  • N. Kopell
  • Brain Theory and Neural Networks, M.A. Arbib, ed…
  • 1995
1 Excerpt

Similar Papers

Loading similar papers…