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Seung Kee Han, Seon Hee Park, Tae Gyu Yim, Seunghwan Kim, and Seunghwan Kim

Chaotic bursting behavior of coupled neural oscillators
Seung Kee Han tex2html_wrap_inline2570 , Seon Hee Park tex2html_wrap_inline2366 , Tae Gyu Yim tex2html_wrap_inline2370 ,
Seunghwan Kim tex2html_wrap_inline2366 , and Seunghwan Kim tex2html_wrap_inline2420
tex2html_wrap_inline2366 Research Dept., ETRI, Yusong-Gu, Taejon, 305-600, Korea
tex2html_wrap_inline2370 Dept. of Physics, Chungbuk National University, Cheongju, Chungbuk, 360-763, Korea
tex2html_wrap_inline2420 Dept. of Physics, Pohang University of Science and Technology, Pohang, 790-784, Korea

Usually, diffusive coupling of nonlinear oscillators in one dynamical variable leads to synchronization of oscillators. We studied a model of coupled neural oscillators in which diffusive coupling in voltage, unexpectedly, leads to dephasing of oscillators [1,2]. We examined the general conditions under which dephasing through diffusive interaction will occur.

Using the Morris-Lecar [3] system, we showed [2] that such systems with dephasing limit cycles lead to a new bursting behavior: oscillators switch between high and low oscillation amplitude. This occurs because the interaction is such that oscillators tend to synchronize for sufficient small oscillation amplitude, while they tend to desynchronize once their oscillation amplitude has become large. It is noted that the single neuron is regularly firing but bursting when coupled with other neurons. Thus the mutual coupling between neurons plays the role of the additional slow variables in the conventional bursting mechanism [4], where the additional slow variables switch the fast dynamics between the steady state and oscillatory state.

To analyze this behavior, we studied diffusively coupled neural oscillators. For a large coupling constant tex2html_wrap_inline2996 , diffusively coupled neural oscillators are perfectly synchronized on the limit cycle of a single oscillator. While for a small tex2html_wrap_inline2996 , the oscillators are homogeneously distributed on the limit cycle because of dephasing between oscillators. For the intermediate values of tex2html_wrap_inline2996 , the bursting behavior occurs, which shows various chaotic behavior depending on tex2html_wrap_inline2996 . To characterize the chaotic bursting behavior, we introduced a set of mean activities. >From Poincare sections, we found [5] a period-doubling route to chaos for 3-diffusively coupled neural oscillators. We observed that the chaotic behavior arises from the competition between the property of limit cycle of the single oscillator and that of the diffusive coupling among the oscillators.

  1. A. Sherman and J. Rinzel, Proc. Nat. Acad. Sci. (USA), 89 (1992) 2471.
  2. S. K. Han, C. Kurrer and Y. Kuramoto, Phys. Rev. Lett., 75 (1995) 3190.
  3. C. Morris and H. Lecar, Biophys. J., 35 (1981) 193.
  4. T. R. Chay and J. Rinzel, Biophys. J., 47 (1985) 357.
  5. S. K. Han, S. H. Park, T. G. Yim, S. Kim, and S. Kim, preprint (1995).


next up previous
Next: Hänggi P. Up: Book of Abstracts Previous: Halfmann J.Schutz R., Muller G.

Book of abstracts
ICND-96