Dynamics of autonomous stochastic resonance in neural period adding bifurcation scenarios. (English) Zbl 1038.92007

Summary: New firing patterns, composed of a stochastic alternation of two periodic bursts, were generated near each bifurcation point of period adding bifurcation scenarios without chaos in the experimental neural pacemaker, in the stochastic Chay model, but not in the deterministic model. It was a stochastic transition between two neighboring bursting and exhibited approximate integer multiple characteristics. Autonomous stochastic resonance (ASR) was verified to be the cause of the generation of this stochastic alternation pattern in the stochastic Chay model. The stochastic transition between two periodic superthreshold bursts generated near a critical phase in the two trajectories was the underlying basis of the effect of ASR. The results showed that except the Hopf bifurcation point, ASR could be generated in a series of period adding bifurcation points, and indicated that noise played more extensive roles in neural coding than recognized before.


92C20 Neural biology
92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] Ren, W.; Hu, S. J.; Zhang, B. J.; Xu, J. X., Int. J. Bifur. Chaos, 7, 1867 (1997)
[2] Chay, T. R., Physica D, 16, 233 (1985) · Zbl 0582.92007
[3] Fan, Y. S.; Chay, T. R., Biol. Cybern., 71, 417 (1994) · Zbl 0805.92005
[4] Chay, T. R.; Fan, Y. S.; Lee, Y. S., Int. J. Bifur. Chaos, 5, 595 (1995) · Zbl 0885.92019
[5] Fan, Y. S.; Holden, A. V., Chaos Solitons Fractals, 3, 439 (1993) · Zbl 0777.92003
[6] Izhikevich, E. M., Int. J. Bifur. Chaos, 10, 1171 (2000) · Zbl 1090.92505
[7] Yang, M. H.; Gu, H. G.; Li, L.; Liu, Z. Q.; Ren, W., NeuroReport, 14 (2003), in press
[8] Li, L.; Gu, H. G.; Yang, M. H.; Liu, Z. Q.; Ren, W., Int. J. Bifur. Chaos, 14 (2004), in press
[9] Longtin, A.; Bulsara, A.; Moss, F., Phys. Rev. Lett., 67, 656 (1991)
[10] Makarov, V. A.; Nekorkin, V. I.; Velarde, M. G., Phys. Rev. Lett., 86, 3431 (2001)
[11] Gu, H. G.; Ren, W.; Lu, Q. S.; Wu, S. G.; Yang, M. H.; Chen, W. J., Phys. Lett. A, 285, 63 (2001)
[12] Yang, Z. Q.; Lu, Q. S.; Gu, H. G.; Ren, W., Phys. Lett. A, 299, 499 (2002) · Zbl 0996.92002
[13] Longtin, A., Phys. Rev. E, 55, 868 (1997)
[14] Wu, S. G.; Ren, W.; He, K. F.; Huang, Z. Q., Phys. Lett. A, 279, 347 (2001) · Zbl 0979.92012
[15] Gu, H. G.; Yang, M. H.; Li, L.; Liu, Z. Q.; Ren, W., NeuroReport, 13, 1657 (2002)
[16] Douglass, J. K.; Wilkens, L.; Pantazelou, E., Nature, 365, 337 (1993)
[17] Wiesenfeld, K.; Pierson, D.; Pantazelo, E., Phys. Rev. Lett., 72, 2125 (1994)
[18] Ren, W.; Gu, H. G.; Jian, Z.; Lu, Q. S.; Yang, M. H., NeuroReport, 12, 2121 (2001)
[19] Benzi, R.; Sutera, S.; Vulpiani, A., J. Phys. A, 14, L453 (1981)
[20] Hu, G.; Ditzinger, T.; Ning, C. Z., Phys. Rev. Lett., 71, 807 (1993)
[21] Bennett, G. T.; Xie, Y. K., Pain, 33, 87 (1988)
[22] Mannella, R.; Palleschi, V., Phys. Rev. A, 40, 3381 (1989)
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