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Taking into account sodium and potassium ion channel noises, the evolution of the patterns of neuronal networks is investigated. No matter what kind of ion channel noise is working, with coupling coefficient increasing, the spatiotemporal patterns of the neuronal network can be evolved into spiral waves when temperature and noise strength are given, and there is a coupling coefficient threshold for forming a spiral wave. The analysis shows that sodium ion channel noise contributes to the formation of spiral waves in neurons network, while the potassium ion channel noise is not conducive to the formation of spiral waves. In addition, it is found that lower temperature can make the neurons network more sensitive to noise. Finally, the transformation of spiral waves into target waves, in the case of specific parameters is discussed.
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Keywords:
- Hodgkin-Huxley model /
- ion channel noise /
- spatiotemporal patterns /
- spiral waves
[1] Narahashi T, Anderson C N, MooreWJ 1967 The Journal of General Physiology 50 1413
[2] Song Y L 2010 Acta Phys. Sin. 59 2334 (in Chinese) [宋艳丽 2010 59 2334]
[3] Armstrong M C, Binstock L 1665 The Journal of General Physiology 48 859
[4] Steinmetz N P, Manwaniand A, Koch C 2000 Journal of Computational Neuroscience 9 133
[5] Shou T D 2001 Neurobiology (Beijing: Higher Education Press) p40 (in Chinese) [寿天德 2001 神经生物学 (北京: 高等教育出版社) 第40页]
[6] Shepherd G M 1998 Neurobiology 2nd ed. (New York: Oxford University Press) p42
[7] Hodgkin A L, Huxley A F 1952 J. Physiol. 116 449
[8] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[9] Correa A M , Bezanilla F, Latorre R 1992 Biophys. J. 61 1332
[10] Gerhard Schmid, Igor Goychuk 2004 Physica A 344 665
[11] Armstrong M C, Hille B 1972 The Journal of General Physiology 59 388
[12] Schmid G, Goychuk I, Hanggi P 2001 Europhys. Lett. 56 22
[13] Gong Y B, Xie Y H, Xu B and Ma X G 2009 Sci China Ser B 52 20.
[14] Gong Y B, Xu B, Ma X G, Han J Q, 2008 Sci China Ser B 38 104 (in Chinese) [龚玉兵, 徐舶, 马晓光, 韩吉衢 2008 中国科学 B 38 104]
[15] Qiao X Y, Li G, Lin L, He B J 2007 Acta Phys. Sin. 56 2448 (in Chinese) [乔晓艳, 李刚, 林凌, 贺秉军 56 2448]
[16] Driessche W V 1984 J. Physiol. 356 79
[17] Martyn P N, Alexander V P 2004 Prog. Biophys. Mol. Bio. 85 501
[18] Fenton F H, Cherry E M, Hasting H M 2002 Chaos 12 852
[19] Liu S Q, Lu Q S, Wang Q 1998 Acta. Phys. Sin. 47 1057 (in Chinese) [刘深泉, 陆启韶, 王琪 1998 47 1057]
[20] Zhang G Y, Ma J, Gan Z N, Chen Y 2008 Acta. Phys. Sin. 57 6815 (in Chinese) [张国勇, 马军, 甘正宁, 陈勇 2008 57 6815]
[21] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Journal of Dynamics and Control. 7 230 (in Chinese) [李玉叶, 张慧敏, 魏春玲, 杨明浩, 古华光, 任维 2009 动力学与控制学报 7 230]
[22] Liu S B, Wu Y, 2010 Journal of Dynamics and Control 8 284 (in Chinese) [刘少宝, 吴莹 2010 动力学与控制学报 8 284]
[23] Du M M, Wu Y, Pang J Z 2010 The Third International Conference on Dynamics, Vibration and Control (ICDVC-2010)
[24] Sun X J, Lei J Z, Perc M, Lu Q S, Lv S J 2011 Eur. Phys. J. B 79 61
[25] Yu G, Ma J, Tang J, Yi M, Jia Y 2008 Int. J. Mod. Phys. B 69 22
[26] Rappel W J 2001 Chaos 11 71
[27] Qu Z L, Kil J, Xie F G, Garfinlel A, N.Weiss J 2000 Biophysical Journal 78 2761
[28] Martyn P N, Alexander V P 2004 Rrog. Biophy. Mol. Bio. 85 501
[29] Sinha S, Pande A, Pandit R 2001 Phys. Rev. Lett. 86 3678
[30] Yang J Z, Garfinkel A 2003 Phys. Rev. E 68 066312
[31] Yang J Z, Xie F G, Qu Z L 2003 Phys. Rev. Lett. 91 148302
[32] Martin Hall G, Daniel J. Gauthier 2002 Phys. Rev. Lett. 88 198102
[33] Hu G, Xiao J H, Chua L O, Ladislav Pivka 1998 Phys. Rev. Lett. 80 1884
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[1] Narahashi T, Anderson C N, MooreWJ 1967 The Journal of General Physiology 50 1413
[2] Song Y L 2010 Acta Phys. Sin. 59 2334 (in Chinese) [宋艳丽 2010 59 2334]
[3] Armstrong M C, Binstock L 1665 The Journal of General Physiology 48 859
[4] Steinmetz N P, Manwaniand A, Koch C 2000 Journal of Computational Neuroscience 9 133
[5] Shou T D 2001 Neurobiology (Beijing: Higher Education Press) p40 (in Chinese) [寿天德 2001 神经生物学 (北京: 高等教育出版社) 第40页]
[6] Shepherd G M 1998 Neurobiology 2nd ed. (New York: Oxford University Press) p42
[7] Hodgkin A L, Huxley A F 1952 J. Physiol. 116 449
[8] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[9] Correa A M , Bezanilla F, Latorre R 1992 Biophys. J. 61 1332
[10] Gerhard Schmid, Igor Goychuk 2004 Physica A 344 665
[11] Armstrong M C, Hille B 1972 The Journal of General Physiology 59 388
[12] Schmid G, Goychuk I, Hanggi P 2001 Europhys. Lett. 56 22
[13] Gong Y B, Xie Y H, Xu B and Ma X G 2009 Sci China Ser B 52 20.
[14] Gong Y B, Xu B, Ma X G, Han J Q, 2008 Sci China Ser B 38 104 (in Chinese) [龚玉兵, 徐舶, 马晓光, 韩吉衢 2008 中国科学 B 38 104]
[15] Qiao X Y, Li G, Lin L, He B J 2007 Acta Phys. Sin. 56 2448 (in Chinese) [乔晓艳, 李刚, 林凌, 贺秉军 56 2448]
[16] Driessche W V 1984 J. Physiol. 356 79
[17] Martyn P N, Alexander V P 2004 Prog. Biophys. Mol. Bio. 85 501
[18] Fenton F H, Cherry E M, Hasting H M 2002 Chaos 12 852
[19] Liu S Q, Lu Q S, Wang Q 1998 Acta. Phys. Sin. 47 1057 (in Chinese) [刘深泉, 陆启韶, 王琪 1998 47 1057]
[20] Zhang G Y, Ma J, Gan Z N, Chen Y 2008 Acta. Phys. Sin. 57 6815 (in Chinese) [张国勇, 马军, 甘正宁, 陈勇 2008 57 6815]
[21] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Journal of Dynamics and Control. 7 230 (in Chinese) [李玉叶, 张慧敏, 魏春玲, 杨明浩, 古华光, 任维 2009 动力学与控制学报 7 230]
[22] Liu S B, Wu Y, 2010 Journal of Dynamics and Control 8 284 (in Chinese) [刘少宝, 吴莹 2010 动力学与控制学报 8 284]
[23] Du M M, Wu Y, Pang J Z 2010 The Third International Conference on Dynamics, Vibration and Control (ICDVC-2010)
[24] Sun X J, Lei J Z, Perc M, Lu Q S, Lv S J 2011 Eur. Phys. J. B 79 61
[25] Yu G, Ma J, Tang J, Yi M, Jia Y 2008 Int. J. Mod. Phys. B 69 22
[26] Rappel W J 2001 Chaos 11 71
[27] Qu Z L, Kil J, Xie F G, Garfinlel A, N.Weiss J 2000 Biophysical Journal 78 2761
[28] Martyn P N, Alexander V P 2004 Rrog. Biophy. Mol. Bio. 85 501
[29] Sinha S, Pande A, Pandit R 2001 Phys. Rev. Lett. 86 3678
[30] Yang J Z, Garfinkel A 2003 Phys. Rev. E 68 066312
[31] Yang J Z, Xie F G, Qu Z L 2003 Phys. Rev. Lett. 91 148302
[32] Martin Hall G, Daniel J. Gauthier 2002 Phys. Rev. Lett. 88 198102
[33] Hu G, Xiao J H, Chua L O, Ladislav Pivka 1998 Phys. Rev. Lett. 80 1884
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