Inhibitory effect induced by fractional Gaussian noise in neuronal system

doi:10.1088/1674-1056/ac6332

中国物理B ›› 2023, Vol. 32 ›› Issue (1): 10203-010203.doi: 10.1088/1674-1056/ac6332

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

收稿日期:2022-01-17 修回日期:2022-03-13 接受日期:2022-04-01 出版日期:2022-12-08 发布日期:2022-12-08
通讯作者: Dong-Xi Li E-mail:dxli0426@126.com
基金资助:
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).

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

Received:2022-01-17 Revised:2022-03-13 Accepted:2022-04-01 Online:2022-12-08 Published:2022-12-08
Contact: Dong-Xi Li E-mail:dxli0426@126.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: inhibitory effect, inverse stochastic resonance, fractional Gaussian noise, neuronal system

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.

Key words: inhibitory effect, inverse stochastic resonance, fractional Gaussian noise, neuronal system

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)

Zhi-Kun Li(李智坤) and Dong-Xi Li(李东喜). Inhibitory effect induced by fractional Gaussian noise in neuronal system[J]. 中国物理B, 2023, 32(1): 10203-010203.

Zhi-Kun Li(李智坤) and Dong-Xi Li(李东喜). Inhibitory effect induced by fractional Gaussian noise in neuronal system[J]. Chin. Phys. B, 2023, 32(1): 10203-010203.

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Inhibitory effect induced by fractional Gaussian noise in neuronal system

Inhibitory effect induced by fractional Gaussian noise in neuronal system

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