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The influence of noise on the dynamics of a two-dimensional neural map with self-sustained subthreshold oscillations is studied by numerical simulation. When the injected current is absent and the control parameter is located in the silence region, numerical results show that stochastic oscillations of the membrane potential can be induced by noise. Moreover, the coherence of such oscillations shows two maxima with the variation of the noise strength. The effect of control parameter on the dynamics of the system has also been investigated. Interestingly, it is found that the occurrence of coherence bi-resonance is closely associated with the distinct characteristics of the bifurcation of the deterministic dynamics.
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Keywords:
- two-dimensional neural map /
- coherence bi-resonance /
- Gaussian white noise /
- subthreshold oscillations
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[1] Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[2] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[3] Wang B H, Lu Q S, Lü S J, Lang X F 2009 Chin. Phys. B 18 872
[4] Xing Z C, Xu W, Rong H W, Wang B Y 2009 Acta Phys. Sin. 58 824 (in Chinese) [邢真慈、徐 伟、戎海武、王宝燕 2009 58 824]
[5] Lin M, Fang L M, Zheng Y J 2009 Chin. Phys. B 18 1725
[6] Wang H Q, Yu L C, Chen Y 2009 Acta Phys. Sin. 58 5070 (in Chinese) [王慧巧、俞连春、陈 勇 2009 58 5070]
[7] Wang C Q, Xu W, Zhang N M, Li H Q 2009 2008 Acta Phys. Sin. 57 749 (in Chinese) [王朝庆、徐 伟、张娜敏、李海泉 2009 57 749]
[8] Hu G, Ditzinger T, Ning C Z, Haken H 1993 Phys. Rev. Lett. 71 807
[9] Pikovsky A, Kurths J 1997 Phys. Rev. Lett. 78 775
[10] Jiang Y, Zhong S, Xin H 2000 J. Phys. Chem. A 104 8521
[11] Pikovsky A, Zaikin A, de la Casa M A 2002 Phys. Rev. Lett. 88 050601
[12] Levin J E, Miller J P 1996 Nature 380 165
[13] Narins P M 2001 Nature 410 644
[14] Song Y, Zhao T J, Liu J W, Wang X Q, Zhan Y 2006 Acta Phys. Sin. 55 4020 (in Chinese) [宋 杨、赵同军、刘金伟、王向群、展 永 2006 55 4020]
[15] Wang M S 2009 Acta Phys. Sin. 58 6833 (in Chinese) [汪茂胜 2009 58 6833]
[16] Wang M S, Hou Z H, Xin H W 2004 ChemPhysChem 5 1602
[17] Wang M S, Hou Z H, Xin H W 2005 Phys. Lett. A 334 93
[18] Shen C S, Zhang J Q, Chen H S 2007 Acta Phys. Sin. 56 6315 (in Chinese) [申传胜、张季谦、陈含爽 2007 56 6315]
[19] Ma J, Li H Y, Hou Z H, Xin H W 2008 Chin. J. Chem. Phys. 21 521
[20] Rulkov N F 2002 Phys. Rev. E 65 041922
[21] Shilnikov A L, Rulkov N F 2004 Phys. Lett. A 328 177
[22] Hou Z H, Xin H W 2003 J. Chem. Phys. 119 11508
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