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September  2011, 16(2): 607-621. doi: 10.3934/dcdsb.2011.16.607

Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking

Qingyun Wang 1, , Xia Shi 2, and  Guanrong Chen 3,

1. 

Department of Dynamics and Control, Beihang University, Beijing 100191, China
2. 

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
3. 

Department of Electronic Engineering, City University of Hong Kong, Hong Kong

Received  December 2009 Revised  September 2010 Published  June 2011

We study the evolution of spatiotemporal dynamics and synchronization transition on small-world Hodgkin-Huxley (HH) neuronal networks that are characterized with channel noises, ion channel blocking and information transmission delays. In particular, we examine the effects of delay on spatiotemporal dynamics over neuronal networks when channel blocking of potassium or sodium is involved. We show that small delays can detriment synchronization in the network due to a dynamic clustering anti-phase synchronization transition. We also show that regions of irregular and regular wave propagations related to synchronization transitions appear intermittently as the delay increases, and the delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony. In addition, we show that the fraction of sodium or potassium channels can play a key role in dynamics of neuronal networks. Furthermore, We found that the fraction of sodium and potassium channels has different impacts on spatiotemporal dynamics of neuronal networks, respectively. Our results thus provide insights that could facilitate the understanding of the joint impact of ion channel blocking and information transmission delays on the dynamical behaviors of realistic neuronal networks.
Keywords: synchronization., time delay, Neural network.
Mathematics Subject Classification: 76R10, 76F7.
Citation: Qingyun Wang, Xia Shi, Guanrong Chen. Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 607-621. doi: 10.3934/dcdsb.2011.16.607
References:
[1]

PNAS, 51 (2006), 19219-19220. doi: 10.1073/pnas.0609523103.  Google Scholar

[2]

Oxford Univ. Press, New York, 1995.  Google Scholar

[3]

Oxford Univ. Press, New York, 2003.  Google Scholar

[4]

Nature, 10 (2009), 186-198.  Google Scholar

[5]

Trends Cogn. Sci., 8 (2004), 418-425. doi: 10.1016/j.tics.2004.07.008.  Google Scholar

[6]

Trends Cogn. Sci., 12 (2006), 512-523.  Google Scholar

[7]

Clin. Neurophysiol., 118 (2007), 2317-2331. doi: 10.1016/j.clinph.2007.08.010.  Google Scholar

[8]

Phys. Usp., 39 (1996), 337-362. doi: 10.1070/PU1996v039n04ABEH000141.  Google Scholar

[9]

Reviews of Modern Physics, 78 (2006), 1213-1265. doi: 10.1103/RevModPhys.78.1213.  Google Scholar

[10]

Computational Methods in Neural Modeling, 2686 (2003), 46-53. doi: 10.1007/3-540-44868-3_7.  Google Scholar

[11]

Phys. Rev. Lett., 87 (2001), 098101. doi: 10.1103/PhysRevLett.87.098101.  Google Scholar

[12]

Cambridge University Press, Cambridge, 2001. doi: 10.1017/CBO9780511755743.  Google Scholar

[13]

New J. Phys, 9 (2007), 1-11. doi: 10.1088/1367-2630/9/10/383.  Google Scholar

[14]

Phys. Lett. A, 298 (2002), 319-324. doi: 10.1016/S0375-9601(02)00575-3.  Google Scholar

[15]

Europhys. Lett., 83 (2008), 50008. doi: 10.1209/0295-5075/83/50008.  Google Scholar

[16]

Chaos, 16 (2006), 013113. doi: 10.1063/1.2148387.  Google Scholar

[17]

Physica A, 374 (2007), 869-878. doi: 10.1016/j.physa.2006.08.062.  Google Scholar

[18]

Phys. Rev. Lett., 97 (2006), 238103. doi: 10.1103/PhysRevLett.97.238103.  Google Scholar

[19]

3rd edition, Sinauer Associates, Sundrland, MA, 2001.  Google Scholar

[20]

Physica A, 389 (2010), 349-357. doi: 10.1016/j.physa.2009.09.033.  Google Scholar

[21]

Europhys. Lett., 86 (2009), 40008. doi: 10.1209/0295-5075/86/40008.  Google Scholar

[22]

Chin. Phys. Lett., 3 (2005), 543-546.  Google Scholar

[23]

Phys. Rev. E, 71 (2005), 061904. doi: 10.1103/PhysRevE.71.061904.  Google Scholar

[24]

Nonlinear Biomedical Physics, 1 (2007), 1-9. doi: 10.1186/1753-4631-1-2.  Google Scholar

[25]

Discrete and Continuous Dynamical Systems-Series B, 9 (2008), 397-413.  Google Scholar

[26]

Discrete and Continuous Dynamical Systems-Series B, 14 (2010), 275-288.  Google Scholar

[27]

Phys. Rev. E, 80 (2009), 026206. doi: 10.1103/PhysRevE.80.026206.  Google Scholar

[28]

J Physiol, 117 (1952), 500-544.  Google Scholar

[29]

Phys. Rev. E., 69 (2004), 011909. doi: 10.1103/PhysRevE.69.011909.  Google Scholar

[30]

Chem. Phys. Chem., 6 (2005), 1042-1047. doi: 10.1002/cphc.200500051.  Google Scholar

[31]

Phys. Rev. E, 73 (2006), 046137. doi: 10.1103/PhysRevE.73.046137.  Google Scholar

[32]

Phys. Rev. E., 65 (2001), 016209. doi: 10.1103/PhysRevE.65.016209.  Google Scholar

show all references

References:
[1]

PNAS, 51 (2006), 19219-19220. doi: 10.1073/pnas.0609523103.  Google Scholar

[2]

Oxford Univ. Press, New York, 1995.  Google Scholar

[3]

Oxford Univ. Press, New York, 2003.  Google Scholar

[4]

Nature, 10 (2009), 186-198.  Google Scholar

[5]

Trends Cogn. Sci., 8 (2004), 418-425. doi: 10.1016/j.tics.2004.07.008.  Google Scholar

[6]

Trends Cogn. Sci., 12 (2006), 512-523.  Google Scholar

[7]

Clin. Neurophysiol., 118 (2007), 2317-2331. doi: 10.1016/j.clinph.2007.08.010.  Google Scholar

[8]

Phys. Usp., 39 (1996), 337-362. doi: 10.1070/PU1996v039n04ABEH000141.  Google Scholar

[9]

Reviews of Modern Physics, 78 (2006), 1213-1265. doi: 10.1103/RevModPhys.78.1213.  Google Scholar

[10]

Computational Methods in Neural Modeling, 2686 (2003), 46-53. doi: 10.1007/3-540-44868-3_7.  Google Scholar

[11]

Phys. Rev. Lett., 87 (2001), 098101. doi: 10.1103/PhysRevLett.87.098101.  Google Scholar

[12]

Cambridge University Press, Cambridge, 2001. doi: 10.1017/CBO9780511755743.  Google Scholar

[13]

New J. Phys, 9 (2007), 1-11. doi: 10.1088/1367-2630/9/10/383.  Google Scholar

[14]

Phys. Lett. A, 298 (2002), 319-324. doi: 10.1016/S0375-9601(02)00575-3.  Google Scholar

[15]

Europhys. Lett., 83 (2008), 50008. doi: 10.1209/0295-5075/83/50008.  Google Scholar

[16]

Chaos, 16 (2006), 013113. doi: 10.1063/1.2148387.  Google Scholar

[17]

Physica A, 374 (2007), 869-878. doi: 10.1016/j.physa.2006.08.062.  Google Scholar

[18]

Phys. Rev. Lett., 97 (2006), 238103. doi: 10.1103/PhysRevLett.97.238103.  Google Scholar

[19]

3rd edition, Sinauer Associates, Sundrland, MA, 2001.  Google Scholar

[20]

Physica A, 389 (2010), 349-357. doi: 10.1016/j.physa.2009.09.033.  Google Scholar

[21]

Europhys. Lett., 86 (2009), 40008. doi: 10.1209/0295-5075/86/40008.  Google Scholar

[22]

Chin. Phys. Lett., 3 (2005), 543-546.  Google Scholar

[23]

Phys. Rev. E, 71 (2005), 061904. doi: 10.1103/PhysRevE.71.061904.  Google Scholar

[24]

Nonlinear Biomedical Physics, 1 (2007), 1-9. doi: 10.1186/1753-4631-1-2.  Google Scholar

[25]

Discrete and Continuous Dynamical Systems-Series B, 9 (2008), 397-413.  Google Scholar

[26]

Discrete and Continuous Dynamical Systems-Series B, 14 (2010), 275-288.  Google Scholar

[27]

Phys. Rev. E, 80 (2009), 026206. doi: 10.1103/PhysRevE.80.026206.  Google Scholar

[28]

J Physiol, 117 (1952), 500-544.  Google Scholar

[29]

Phys. Rev. E., 69 (2004), 011909. doi: 10.1103/PhysRevE.69.011909.  Google Scholar

[30]

Chem. Phys. Chem., 6 (2005), 1042-1047. doi: 10.1002/cphc.200500051.  Google Scholar

[31]

Phys. Rev. E, 73 (2006), 046137. doi: 10.1103/PhysRevE.73.046137.  Google Scholar

[32]

Phys. Rev. E., 65 (2001), 016209. doi: 10.1103/PhysRevE.65.016209.  Google Scholar

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