Threshold disorder as a source of diverse and complex behavior in random nets

McGuire PC, Bohr H, Clark JW, Haschke R, Pershing CL, Rafelski J (2002)
NEURAL NETWORKS 15(10): 1243-1258.

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Abstract
We study the diversity of complex spatio-temporal patterns in the behavior of random synchronous asymmetric neural networks (RSANNs). Special attention is given to the impact of disordered threshold values on limit-cycle diversity and limit-cycle complexity in RSANNs which have ‘normal’ thresholds by default. Surprisingly, RSANNs exhibit only a small repertoire of rather complex limit-cycle patterns when all parameters are fixed. This repertoire of complex patterns is also rather stable with respect to small parameter changes. These two unexpected results may generalize to the study of other complex systems. In order to reach beyond this seemingly disabling ‘stable and small’ aspect of the limit-cycle repertoire of RSANNs, we have found that if an RSANN has threshold disorder above a critical level, then there is a rapid increase of the size of the repertoire of patterns. The repertoire size initially follows a power-law function of the magnitude of the threshold disorder. As the disorder increases further, the limit-cycle patterns themselves become simpler until at a second critical level most of the limit cycles become simple fixed points. Nonetheless, for moderate changes in the threshold parameters, RSANNs are found to display specific features of behavior desired for rapidly responding processing systems: accessibility to a large set of complex patterns.
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McGuire PC, Bohr H, Clark JW, Haschke R, Pershing CL, Rafelski J. Threshold disorder as a source of diverse and complex behavior in random nets. NEURAL NETWORKS. 2002;15(10):1243-1258.
McGuire, P. C., Bohr, H., Clark, J. W., Haschke, R., Pershing, C. L., & Rafelski, J. (2002). Threshold disorder as a source of diverse and complex behavior in random nets. NEURAL NETWORKS, 15(10), 1243-1258.
McGuire, P. C., Bohr, H., Clark, J. W., Haschke, R., Pershing, C. L., and Rafelski, J. (2002). Threshold disorder as a source of diverse and complex behavior in random nets. NEURAL NETWORKS 15, 1243-1258.
McGuire, P.C., et al., 2002. Threshold disorder as a source of diverse and complex behavior in random nets. NEURAL NETWORKS, 15(10), p 1243-1258.
P.C. McGuire, et al., “Threshold disorder as a source of diverse and complex behavior in random nets”, NEURAL NETWORKS, vol. 15, 2002, pp. 1243-1258.
McGuire, P.C., Bohr, H., Clark, J.W., Haschke, R., Pershing, C.L., Rafelski, J.: Threshold disorder as a source of diverse and complex behavior in random nets. NEURAL NETWORKS. 15, 1243-1258 (2002).
McGuire, Patrick C., Bohr, Henrik, Clark, John W., Haschke, Robert, Pershing, Chris L., and Rafelski, Johann. “Threshold disorder as a source of diverse and complex behavior in random nets”. NEURAL NETWORKS 15.10 (2002): 1243-1258.
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Reverberating activity in a neural network with distributed signal transmission delays.
Omi T, Shinomoto S., Phys Rev E Stat Nonlin Soft Matter Phys 76(5 Pt 1), 2007
PMID: 18233688

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