doi:10.1088/1674-1056/ac6332

Inhibitory effect induced by fractional Gaussian noise in neuronal system

doi: 10.1088/1674-1056/ac6332

Li Zhi-Kun^1
,,
Li Dong-Xi²

1.
College of Mathematics, Taiyuan University of Technology,Taiyuan 030024,China
2.
College of Data Science, Taiyuan University of Technology,Taiyuan 030024,China

摘要

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.
- inhibitory effect /
- inverse stochastic resonance /
- fractional Gaussian noise /
- neuronal system

HTML全文

1. Fractional Brownian motion B _H ( t) with different Hurst index, H takes 0.3, 0.5, and 0.7.

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2. Spectral density of fractional Gaussian noise G _H ( t) with different Hurst index, H takes 0.3, 0.5, 0.7.

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3. Time series plots of the neuronal model at different noise intensity, where external current I = 7 and Hurst index H = 0.6, D takes 0.1, 5, 9.

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4. Time series plots of the neuronal model at different Hurst index, where external current I = 7 and noise intensity D = 0.6, H takes 0.3, 0.7, 0.9.

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5. The average firing rate R varies with noise intensity D at different parameters. (a) Fix the external current as I = 7, Hurst index H makes 0.3, 0.5, 0.7, 0.9. (b) Fix the Hurst index as H = 0.6, external current I makes 5.5, 6.6, 8, 9.5.

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6. Average firing rate R varies with the Hurst index H under different parameters. (a) External current I = 7, noise intensity D makes 0.1, 1, 4, 7.5. (b) Noise intensity D = 0.6, external current I makes 5.5, 6.6, 8, 9.5.

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7. (a) Average discharge rate R with noise intensity D and Hurst index H. (b) Average discharge rate R with Hurst index H and current intensity I.

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8. (a) Histogram of peak-to-peak intervals under different Hurst index, I = 7 and D = 0.6 are fixed, H takes 0.3, 0.7, 0.8. (b) Histograms of peak-to-peak intervals at different noise intensity, I = 7 and H = 0.6 are fixed, D takes 0.1, 5, 8.

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