Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:C1L-D

Session:

Number:594

Dynamical Robustness in Synaptically Coupled Neuronal Networks

Gouhei Tanaka,  Kai Morino,  Kazuyuki Aihara,  

pp.594-597

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.594

PDF download (291.8KB)

Tolerance of biological networks against local perturbations is still not completely understood, because both structure and dynamics are often complex in such networks. Here we study the role of synaptic connections in robustness of dynamic activities in neuronal network models. We show that the dynamical robustness varies depending on the strength and the number of the synaptic connections. We also demonstrate that homogeneous networks are more tolerant than heterogeneous networks from the dynamical robustness viewpoint. This case study would contribute to understanding robustness of biological networks.

[1] H. Kitano, “Systems biology: a brief overview,” Science, vol. 295, 1662-1664, 2002.

[2] H. Kitano, “Biological robustness,” Nat. Rev. Genet., vol. 5, 826-837, 2004.

[3] H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabási, “The large-scale organization of metabolic networks,” Nature, vol. 407, 651-654, 2000.

[4] H. Jeong, S. Mason, A.-L. Barabási, and Z. N. Oltvai, “Lethality and centrality in protein networks,” Nature, vol. 411, 41-42, 2001.

[5] R. Albert, “Scale-free networks in cell biology,” J. Cell Sci., vol. 118, 4947-4957, 2005.

[6] E. Bullmore and O. Sporns, “Complex brain networks: graph theoretical analysis of structural and functional systems,” Nat. Rev. Neurosci., vol. 10, 186-198, 2009.

[7] A.-L. Barabási and Z. N. Oltvai, “Network Biology: Understanding the Cell’s Functional Organization,” Nat. Rev. Genet., vol. 5, 101-113, 2004.

[8] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang, “Complex networks: structure and dynamics,” Phys. Rep., vol. 424, 175-308, 2006.

[9] G. Tanaka, K. Morino, and K. Aihara “Dynamical robustness in complex networks: the crucial role of low-degree nodes,” Sci. Rep., vol. 2, 223, 2012.

[10] H. Daido and K. Nakanishi, “Aging transition and universal scaling in oscillator networks,” Phys. Rev. Lett., vol. 93, 104101, 2004.

[11] D. Pazó and E. Montbrió, “Universal behavior in populations composed of excitable and self-oscillatory elements,” Phys. Rev. E, vol. 73, 055202(R), 2006.

[12] K. Morino, G. Tanaka, and K. Aihara, “Robustness of multilayer oscillator networks,” Phys. Rev. E, vol. 83, 056208, 2011.

[13] C. Morris and H. Lecar, “Voltage oscillations in the barnacle giant muscle fiber,” Biophys. J., vol. 35, 193-213, 1981.

[14] J. Rinzel and B. Ermentrout, “Analysis of neural excitability and oscillations,” 251-292 in C. Koch and I. Segev (eds.) Methods ofo Neuronal Modeling, MIT Press, Cambridge, 1998.

[15] K. Tsumoto, H. Kitajima, T. Yoshinaga, K. Aihara, and H. Kawakami, “Bifurcations in Morris-Lecar neuron model,” Neurocomp., vol. 69, 293-316, 2006.

[16] P. Balenzuela and J. Garcá-Ojalvo, “Role of chemical synapses in coupled neurons with noise,” Phys. Rev. E, vol. 72, 021901, 2005.

[17] P. Erdös and A. Rényi, “On the evolution of random graphs,” Publications of the Mathematical Institute of the Hungarian Academy of Sciences, vol. 5, 17-61, 1960.

[18] A.-L. Barabási and R. Albert. “Emergence of scaling in random networks,” Science, vol. 286, 509-512, 1999.

[19] R. Albert, H. Jeong, and A.-L. Barabási, “Error and attack tolerance of complex networks,” Nature, vol. 406, 378-382, 2000.