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A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP
Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking
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 |
References:
[1] |
O. Sporns and J. C. Honey, Small world inside big brains, PNAS, 51 (2006), 19219-19220.
doi: 10.1073/pnas.0609523103. |
[2] |
R. S. Cajal, "Histology of the Nervous System of Man and Vertebrates," Oxford Univ. Press, New York, 1995. |
[3] |
W. L. Swanson, "Brain Architecture," Oxford Univ. Press, New York, 2003. |
[4] |
E. Bullmore and O. Sporns, Complex brain networks: graph theoretical analysis of structural and functional systems, Nature, 10 (2009), 186-198. |
[5] |
O. Sporns, D. Chialvo, M. Kaiser and C. C. Hilgetag, Organization, development and function of complex brain networks, Trends Cogn. Sci., 8 (2004), 418-425.
doi: 10.1016/j.tics.2004.07.008. |
[6] |
S. D. Bassett and T. E. Bullmore, Small world brain networks, Trends Cogn. Sci., 12 (2006), 512-523. |
[7] |
C. J. Reijneveld, S. C. Ponten, H. W. Berendse and J. C. Stam, The application of graph theoretical analysis to complex networks in the brain, Clin. Neurophysiol., 118 (2007), 2317-2331.
doi: 10.1016/j.clinph.2007.08.010. |
[8] |
H. D. I. Abarbanel, M. I. Rabinovich, A. I. Selverston, M. V. Bazhenov, R. Huerta, M. M. Suschchik and L. L. Rubchinskii, Synchronisation in neural networks, Phys. Usp., 39 (1996), 337-362.
doi: 10.1070/PU1996v039n04ABEH000141. |
[9] |
M. I. Rabinovich, P. Varona, A. I. Selverston and H. D. Abarbanel, Dynamical Principles in Neuroscience, Reviews of Modern Physics, 78 (2006), 1213-1265.
doi: 10.1103/RevModPhys.78.1213. |
[10] |
C. Hauptmann, A. Gail and F. Giannakopoulos, Intermittent burst synchronization in neural networks, Computational Methods in Neural Modeling, 2686 (2003), 46-53.
doi: 10.1007/3-540-44868-3_7. |
[11] |
C. Zhou, J. Kurths and B. Hu, Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise, Phys. Rev. Lett., 87 (2001), 098101.
doi: 10.1103/PhysRevLett.87.098101. |
[12] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511755743. |
[13] |
Q. Y. Wang, Z. S. Duan, L. Huang, G. R. Chen and Q. S. Lu, Pattern formation and firing synchronization in networks of map neurons, New J. Phys, 9 (2007), 1-11.
doi: 10.1088/1367-2630/9/10/383. |
[14] |
O. Kwon and H.-T. Moon, Coherence resonance in small-world networks of excitable cells, Phys. Lett. A, 298 (2002), 319-324.
doi: 10.1016/S0375-9601(02)00575-3. |
[15] |
Q. Y. Wang, Z. S. Duan, M. Perc and G. R. Chen, Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability, Europhys. Lett., 83 (2008), 50008.
doi: 10.1209/0295-5075/83/50008. |
[16] |
G. Tanakaa, B. Ibarz, M. A. F. Sanjuan and K. Aihara, Synchronization and propagation of bursts in networks of coupled map neurons, Chaos, 16 (2006), 013113.
doi: 10.1063/1.2148387. |
[17] |
Q. Y. Wang, Q. S. Lu and G. R. Chen, Ordered bursting synchronization and complex wave propagation in a ring neuronal network, Physica A, 374 (2007), 869-878.
doi: 10.1016/j.physa.2006.08.062. |
[18] |
C. S. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag and J. Kurths, Hierarchical organization unveiled by functional connectivity in complex brain networks, Phys. Rev. Lett., 97 (2006), 238103.
doi: 10.1103/PhysRevLett.97.238103. |
[19] |
H. Hill, "Ionic Channels of Excitable Membranes," 3rd edition, Sinauer Associates, Sundrland, MA, 2001. |
[20] |
Y. B. Gong, Y. H. Hao and Y. H. Xie, Channel blocking-optimized spiking activity of Hodgkin-Huxley neurons on random networks, Physica A, 389 (2010), 349-357.
doi: 10.1016/j.physa.2009.09.033. |
[21] |
M. Ozer, M. Perc and M. Uzuntarl, Controlling the spontaneous spiking regularity via channel blockinging on Newman-Watts networks of Hodgkin-Huxley neurons, Europhys. Lett., 86 (2009), 40008.
doi: 10.1209/0295-5075/86/40008. |
[22] |
Q. Y. Wang and Q. S. Lu, Time Delay-Enhanced Synchronization and Regularization in Two Coupled Chaotic Neurons, Chin. Phys. Lett., 3 (2005), 543-546. |
[23] |
E. Rossoni, Y. H. Chen, M. Z. Ding and J. F. Feng, Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed coupling, Phys. Rev. E, 71 (2005), 061904.
doi: 10.1103/PhysRevE.71.061904. |
[24] |
A. S. Landsman and I. B. Schwartz, Synchronized dynamics of cortical neurons with time-delay feedback, Nonlinear Biomedical Physics, 1 (2007), 1-9.
doi: 10.1186/1753-4631-1-2. |
[25] |
S. Q. Ma, Z. S. Feng and Q. S. Lu, A two-parameter geometrical criteria for delay differential equations, Discrete and Continuous Dynamical Systems-Series B, 9 (2008), 397-413. |
[26] |
F. K. Wu and Y. Z. Hu, Stochastic Lotka-Volterra system with unbounded distributed delay, Discrete and Continuous Dynamical Systems-Series B, 14 (2010), 275-288. |
[27] |
Q. Y. Wang, M. Perc, Z. S. Duan and G. R. Chen, Synchronization transitions on scale-free neuronal networks due to finite information transmission delays, Phys. Rev. E, 80 (2009), 026206.
doi: 10.1103/PhysRevE.80.026206. |
[28] |
A. L. Hodgkin and A. F. Huxley, Quantitative description of membrane and its application to conduction and excitation in nerve, J Physiol, 117 (1952), 500-544. |
[29] |
S. T. Wang, F. Liu, W. Wang and Y. G. Yu, Impact of spatially correlated noise on neuronal firing, Phys. Rev. E., 69 (2004), 011909.
doi: 10.1103/PhysRevE.69.011909. |
[30] |
Y. B. Gong, M. S. Wang, Z. H. Hou and H. W. Xin, Optimal Spike Coherence and Synchronization on Complex Hodgkin-Huxley Neuron Networks, Chem. Phys. Chem., 6 (2005), 1042-1047.
doi: 10.1002/cphc.200500051. |
[31] |
Y. B. Gong, B. Xu, Q. Xu, C. L. Yang, T. Q. Ren, Z. H. Hou and H. W Xin, Ordering spatiotemporal chaos in complex thermosensitive neuron networks, Phys. Rev. E, 73 (2006), 046137.
doi: 10.1103/PhysRevE.73.046137. |
[32] |
Z. Gao, B. Hu and G. Hu, Stochastic resonance of small-world networks, Phys. Rev. E., 65 (2001), 016209.
doi: 10.1103/PhysRevE.65.016209. |
show all references
References:
[1] |
O. Sporns and J. C. Honey, Small world inside big brains, PNAS, 51 (2006), 19219-19220.
doi: 10.1073/pnas.0609523103. |
[2] |
R. S. Cajal, "Histology of the Nervous System of Man and Vertebrates," Oxford Univ. Press, New York, 1995. |
[3] |
W. L. Swanson, "Brain Architecture," Oxford Univ. Press, New York, 2003. |
[4] |
E. Bullmore and O. Sporns, Complex brain networks: graph theoretical analysis of structural and functional systems, Nature, 10 (2009), 186-198. |
[5] |
O. Sporns, D. Chialvo, M. Kaiser and C. C. Hilgetag, Organization, development and function of complex brain networks, Trends Cogn. Sci., 8 (2004), 418-425.
doi: 10.1016/j.tics.2004.07.008. |
[6] |
S. D. Bassett and T. E. Bullmore, Small world brain networks, Trends Cogn. Sci., 12 (2006), 512-523. |
[7] |
C. J. Reijneveld, S. C. Ponten, H. W. Berendse and J. C. Stam, The application of graph theoretical analysis to complex networks in the brain, Clin. Neurophysiol., 118 (2007), 2317-2331.
doi: 10.1016/j.clinph.2007.08.010. |
[8] |
H. D. I. Abarbanel, M. I. Rabinovich, A. I. Selverston, M. V. Bazhenov, R. Huerta, M. M. Suschchik and L. L. Rubchinskii, Synchronisation in neural networks, Phys. Usp., 39 (1996), 337-362.
doi: 10.1070/PU1996v039n04ABEH000141. |
[9] |
M. I. Rabinovich, P. Varona, A. I. Selverston and H. D. Abarbanel, Dynamical Principles in Neuroscience, Reviews of Modern Physics, 78 (2006), 1213-1265.
doi: 10.1103/RevModPhys.78.1213. |
[10] |
C. Hauptmann, A. Gail and F. Giannakopoulos, Intermittent burst synchronization in neural networks, Computational Methods in Neural Modeling, 2686 (2003), 46-53.
doi: 10.1007/3-540-44868-3_7. |
[11] |
C. Zhou, J. Kurths and B. Hu, Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise, Phys. Rev. Lett., 87 (2001), 098101.
doi: 10.1103/PhysRevLett.87.098101. |
[12] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511755743. |
[13] |
Q. Y. Wang, Z. S. Duan, L. Huang, G. R. Chen and Q. S. Lu, Pattern formation and firing synchronization in networks of map neurons, New J. Phys, 9 (2007), 1-11.
doi: 10.1088/1367-2630/9/10/383. |
[14] |
O. Kwon and H.-T. Moon, Coherence resonance in small-world networks of excitable cells, Phys. Lett. A, 298 (2002), 319-324.
doi: 10.1016/S0375-9601(02)00575-3. |
[15] |
Q. Y. Wang, Z. S. Duan, M. Perc and G. R. Chen, Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability, Europhys. Lett., 83 (2008), 50008.
doi: 10.1209/0295-5075/83/50008. |
[16] |
G. Tanakaa, B. Ibarz, M. A. F. Sanjuan and K. Aihara, Synchronization and propagation of bursts in networks of coupled map neurons, Chaos, 16 (2006), 013113.
doi: 10.1063/1.2148387. |
[17] |
Q. Y. Wang, Q. S. Lu and G. R. Chen, Ordered bursting synchronization and complex wave propagation in a ring neuronal network, Physica A, 374 (2007), 869-878.
doi: 10.1016/j.physa.2006.08.062. |
[18] |
C. S. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag and J. Kurths, Hierarchical organization unveiled by functional connectivity in complex brain networks, Phys. Rev. Lett., 97 (2006), 238103.
doi: 10.1103/PhysRevLett.97.238103. |
[19] |
H. Hill, "Ionic Channels of Excitable Membranes," 3rd edition, Sinauer Associates, Sundrland, MA, 2001. |
[20] |
Y. B. Gong, Y. H. Hao and Y. H. Xie, Channel blocking-optimized spiking activity of Hodgkin-Huxley neurons on random networks, Physica A, 389 (2010), 349-357.
doi: 10.1016/j.physa.2009.09.033. |
[21] |
M. Ozer, M. Perc and M. Uzuntarl, Controlling the spontaneous spiking regularity via channel blockinging on Newman-Watts networks of Hodgkin-Huxley neurons, Europhys. Lett., 86 (2009), 40008.
doi: 10.1209/0295-5075/86/40008. |
[22] |
Q. Y. Wang and Q. S. Lu, Time Delay-Enhanced Synchronization and Regularization in Two Coupled Chaotic Neurons, Chin. Phys. Lett., 3 (2005), 543-546. |
[23] |
E. Rossoni, Y. H. Chen, M. Z. Ding and J. F. Feng, Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed coupling, Phys. Rev. E, 71 (2005), 061904.
doi: 10.1103/PhysRevE.71.061904. |
[24] |
A. S. Landsman and I. B. Schwartz, Synchronized dynamics of cortical neurons with time-delay feedback, Nonlinear Biomedical Physics, 1 (2007), 1-9.
doi: 10.1186/1753-4631-1-2. |
[25] |
S. Q. Ma, Z. S. Feng and Q. S. Lu, A two-parameter geometrical criteria for delay differential equations, Discrete and Continuous Dynamical Systems-Series B, 9 (2008), 397-413. |
[26] |
F. K. Wu and Y. Z. Hu, Stochastic Lotka-Volterra system with unbounded distributed delay, Discrete and Continuous Dynamical Systems-Series B, 14 (2010), 275-288. |
[27] |
Q. Y. Wang, M. Perc, Z. S. Duan and G. R. Chen, Synchronization transitions on scale-free neuronal networks due to finite information transmission delays, Phys. Rev. E, 80 (2009), 026206.
doi: 10.1103/PhysRevE.80.026206. |
[28] |
A. L. Hodgkin and A. F. Huxley, Quantitative description of membrane and its application to conduction and excitation in nerve, J Physiol, 117 (1952), 500-544. |
[29] |
S. T. Wang, F. Liu, W. Wang and Y. G. Yu, Impact of spatially correlated noise on neuronal firing, Phys. Rev. E., 69 (2004), 011909.
doi: 10.1103/PhysRevE.69.011909. |
[30] |
Y. B. Gong, M. S. Wang, Z. H. Hou and H. W. Xin, Optimal Spike Coherence and Synchronization on Complex Hodgkin-Huxley Neuron Networks, Chem. Phys. Chem., 6 (2005), 1042-1047.
doi: 10.1002/cphc.200500051. |
[31] |
Y. B. Gong, B. Xu, Q. Xu, C. L. Yang, T. Q. Ren, Z. H. Hou and H. W Xin, Ordering spatiotemporal chaos in complex thermosensitive neuron networks, Phys. Rev. E, 73 (2006), 046137.
doi: 10.1103/PhysRevE.73.046137. |
[32] |
Z. Gao, B. Hu and G. Hu, Stochastic resonance of small-world networks, Phys. Rev. E., 65 (2001), 016209.
doi: 10.1103/PhysRevE.65.016209. |
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