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No Access Submitted: 27 February 2017 Accepted: 19 May 2017 Published Online: 06 June 2017

Information-based measures for logical stochastic resonance in a synthetic gene network under Lévy flight superdiffusion

Chaos 27, 063105 (2017); https://doi.org/10.1063/1.4984806
Juan Wu1,2,3, Yong Xu1,2,3,4,a), Haiyan Wang5, and Jürgen Kurths3,4
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ABSTRACT
We investigate the logical information transmission of a synthetic gene network under Lévy flight superdiffusion by an information-based methodology. We first present the stochastic synthetic gene network model driven by a square wave signal under Lévy noise caused by Lévy flight superdiffusion. Then, to quantify the potential of logical information transmission and logical stochastic resonance, we theoretically obtain an information-based methodology of the symbol error rate, the noise entropy, and the mutual information of the logical information transmission. Consequently, based on the complementary “on” and “off” states shown in the logical information transmission for the repressive proteins, we numerically calculate the symbol error rate for logic gates, which demonstrate that the synthetic gene network under Lévy noise can achieve some logic gates as well as logical stochastic resonance. Furthermore, we calculate the noise entropy and the mutual information between the square wave signal and the logical information transmission, which reveal and quantify the potential of logical information transmission and logical stochastic resonance. In addition, we analyze the synchronization degree of the mutual information for the accomplished logical stochastic resonance of two repressive proteins of the synthetic gene network by synchronization variances, which shows that those mutual information changes almost synchronously.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11602003 and 11372247. Y. Xu acknowledges the Alexander von Humboldt Foundation and the Fundamental Research Funds for the Central Universities.

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  1. © 2017 Author(s). Published by AIP Publishing.

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