Summary

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

2012

Session Number:A1L-D

Session:

Number:66

Zero-lag and group synchronization in neural networks

Judith Lehnert,  Thomas Dahms,  Eckehard Schöll,  

pp.66-69

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.66

PDF download (658.7KB)

In the brain, synchronization is a prominent phenomenon associated with several cognitive capacities as well as pathological states like Parkinson's disease or epilepsy. We study the stability of synchronization in delay-coupled neural networks with a master stability approach. In the case of identical nodes and a single delay time, zero-lag synchronization is always, i.e., independently of the particular delay time and coupling strength, stable in excitatory networks. Inhibition can introduce a phase transition to desynchronization, e.g., in small-world or random networks. We then extend the master stability approach to more complex synchronization patterns where the nodes are synchronized in groups with phase lags between these groups. The local dynamics of each group can differ. For example, this approach allows us to use different neuronal models, e.g., for excitatory and inhibitory neurons. Furthermore, time delays and coupling strengths between the different clusters can be chosen nonuniformly allowing for complex dynamics, like bursting patterns, within the synchronization manifold even in the case of identical nodes. We discuss the stability of such patterns. In the case of identical nodes, delay times and coupling strengths, for appropriate topologies we obtain multistability between several cluster states.

[1] W. Singer, Neuron 24, 49 (1999).

[2] P. J. Uhlhaas and W. Singer, Neuron 52, 155 (2006).

[3] S. Coombes and C. Laing, Phil. Trans. R. Soc. A 367, 1117 (2009).

[4] W. Lu and T. Chen, IEEE Trans. Circuits Syst. I 51, 2491 (2004).

[5] M. Timme, T. Geisel, and F. Wolf, Chaos 16, 015108 (2006).

[6] P. Uhlhaas, G. Pipa, B. Lima, L. Melloni, S. Neuenschwander, D. Nikolic, and W. Singer, Front. Integr. Neurosci. 3, 17 (2009).

[7] M. Dhamala, V. K. Jirsa, and M. Ding, Phys. Rev. Lett. 92, 074104 (2004).

[8] V. K. Jirsa, Cogn. Neurodyn. 2, 29 (2008).

[9] J. Lehnert, T. Dahms, P. Hövel, and E. Schöll, Europhys. Lett. 96, 60013 (2011).

[10] F. Sorrentino and E. Ott, Phys. Rev. E 76, 056114 (2007).

[11] T. Dahms, J. Lehnert, and E. Schöll, Phys. Rev. E (2012), in print (arXiv:1203.4916).

[12] L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).

[13] W. Kinzel, A. Englert, G. Reents, M. Zigzag, and I. Kanter, Phys. Rev. E 79, 056207 (2009).

[14] A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, Phys. Rev. Lett. 104, 114102 (2010).

[15] V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, Phys. Rev. Lett. 105, 254101 (2010).

[16] S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, Phys. Rev. Lett. 107, 234102 (2011).

[17] V. Flunkert and E. Schöll, New. J. Phys. 14, 033039 (2012).

[18] C. U. Choe, T. Dahms, P. Hövel, and E. Schöll, Phys. Rev. E 81, 025205(R) (2010).

[19] A. A. Selivanov, J. Lehnert, T. Dahms, P. Hövel, A. L. Fradkov, and E. Schöll, Phys. Rev. E 85, 016201 (2012).

[20] J. Kestler, W. Kinzel, and I. Kanter, Phys. Rev. E 76, 035202 (2007).

[21] J. Kestler, E. Kopelowitz, I. Kanter, and W. Kinzel, Phys. Rev. E 77, 046209 (2008).

[22] E. Schöll, G. Hiller, P. Hövel, and M. A. Dahlem, Phil. Trans. R. Soc. A 367, 1079 (2009).

[23] M. G. Earl and S. H. Strogatz, Phys. Rev. E 67, 036204 (2003).