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Chin. Phys. B, 2023, Vol. 32(1): 010203    DOI: 10.1088/1674-1056/ac6332
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Inhibitory effect induced by fractional Gaussian noise in neuronal system

Zhi-Kun Li(李智坤)1 and Dong-Xi Li(李东喜)2,†
1 College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;
2 College of Data Science, Taiyuan University of Technology, Taiyuan 030024, China
Abstract  We discover a phenomenon of inhibition effect induced by fractional Gaussian noise in a neuronal system. Firstly, essential properties of fractional Brownian motion (fBm) and generation of fractional Gaussian noise (fGn) are presented, and representative sample paths of fBm and corresponding spectral density of fGn are discussed at different Hurst indexes. Next, we consider the effect of fGn on neuronal firing, and observe that neuronal firing decreases first and then increases with increasing noise intensity and Hurst index of fGn by studying the time series evolution. To further quantify the inhibitory effect of fGn, by introducing the average discharge rate, we investigate the effects of noise and external current on neuronal firing, and find the occurrence of inhibitory effect about noise intensity and Hurst index of fGn at a certain level of current. Moreover, the inhibition effect is not easy to occur when the noise intensity and Hurst index are too large or too small. In view of opposite action mechanism compared with stochastic resonance, this suppression phenomenon is called inverse stochastic resonance (ISR). Finally, the inhibitory effect induced by fGn is further verified based on the inter-spike intervals (ISIs) in the neuronal system. Our work lays a solid foundation for future study of non-Gaussian-type noise on neuronal systems.
Keywords:  inhibitory effect      inverse stochastic resonance      fractional Gaussian noise      neuronal system  
Received:  17 January 2022      Revised:  13 March 2022      Accepted manuscript online:  01 April 2022
PACS:  02.50.-r (Probability theory, stochastic processes, and statistics)  
  05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11402157) and Applied Basic Research Programs of Shanxi Province, China (Grant No. 201901D111086).
Corresponding Authors:  Dong-Xi Li     E-mail:

Cite this article: 

Zhi-Kun Li(李智坤) and Dong-Xi Li(李东喜) Inhibitory effect induced by fractional Gaussian noise in neuronal system 2023 Chin. Phys. B 32 010203

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