Summary

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

2012

Session Number:C1L-D

Session:

Number:602

Dynamical Reorganization of Attractor Structure in Neural Networks with Dynamic Synapses

Yuichi Katori,  Kazuyuki Aihara,  

pp.602-605

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.602

PDF download (551.9KB)

We investigate the dynamical properties of a neural network with dynamic synapses, whose transmission efficacy is modulated by short-term plasticity, and we use a mean field model that approximates the population dynamics of spiking neurons. In particular, we consider a neural network with recurrent connections via depression and facilitation synapses, and we analyze the influence of synaptic modulation on the dynamics of synaptic activity via slow-fast analysis with time-parameterized bifurcation parameters. The model is described by three variables: one represents synaptic activity, whereas the other two represent modulation in synaptic transmission efficacy. The variables that represent the synaptic modulation can be considered as slow variables that affect the properties of synaptic activity, which can be regarded as the fast variable. The analysis indicates that an attractor in the fast system corresponding to an active state of the neural network appears or disappears according to the activities of the neural network. The concept of dynamical reorganization of the attractor structure can potentially uncover the mechanism of flexible brain functions.

[1] J. J. Hopfield, “Neurons with graded response have collective computational properties like those of twostate neurons,” P. Natl. Acad. Sci. USA, vol. 81, no. 10, pp. 3088-3092, 1984.

[2] X. J. Wang, “Synaptic basis of cortical persistent activity: the importance of nmda receptors to working memory,” J. Neurosci., vol. 19, no. 21, pp. 9587-603, 1999.

[3] H. Markram, Y. Wang, and M. Tsodyks, “Differential signaling via the same axon of neocortical pyramidal neurons,” P. Natl. Acad. Sci. USA, vol. 95, no. 9, pp. 5323-8, 1998.

[4] Y. Katori, K. Sakamoto, N. Saito, J. Tanji, H. Mushiake, and K. Aihara, “Representational switching by dynamical reorganization of attractor structure in a network model of the prefrontal cortex,” PLoS Comput. Biol., vol. 7, no. 11, e1002266, 2011.

[5] E. Izhikevich, “Neural excitability, spiking and bursting,” Int. J. Bifurcat. Chaos, vol. 10, no. 6, pp. 1171-1266, 2000.

[6] S. Doi, S. Nabetani, and S. Kumagai, “Complex nonlinear dynamics of the hodgkinhuxley equations induced by time scale changes,” Biol. Cybern., vol. 85, no. 1, pp. 51-64, 2001.

[7] M. Tsodyks, K. Pawelzik, and H. Markram, “Neural networks with dynamic synapses,” Neural Comput., vol. 10, no. 4, pp. 821-35, 1998.

[8] G. Mongillo, O. Barak, and M. Tsodyks, “Synaptic theory of working memory,” Science, vol. 319, no. 5869, pp. 1543-6, 2008.