Inhibitory effect induced by fractional Gaussian noise in neuronal system

Li Zhi-Kun; Li Dong-Xi

doi:10.1088/1674-1056/ac6332

Volume 32 Issue 1

May. 2023

Turn off MathJax

Article Contents

JOURNAL OF MECHANICAL ENGINEERING > 2023 > 32(1): 010203.

Li Zhi-Kun, Li Dong-Xi. Inhibitory effect induced by fractional Gaussian noise in neuronal system[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 32(1): 010203. doi: 10.1088/1674-1056/ac6332

Citation:

Li Zhi-Kun, Li Dong-Xi. Inhibitory effect induced by fractional Gaussian noise in neuronal system[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 32(1): 010203. doi: 10.1088/1674-1056/ac6332

Li Zhi-Kun, Li Dong-Xi. Inhibitory effect induced by fractional Gaussian noise in neuronal system[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 32(1): 010203. doi: 10.1088/1674-1056/ac6332

Citation:

Li Zhi-Kun, Li Dong-Xi. Inhibitory effect induced by fractional Gaussian noise in neuronal system[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 32(1): 010203. doi: 10.1088/1674-1056/ac6332

PDF( 0 KB)

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

Received Date: 17 Jan 2022
Available Online: 22 May 2023
Issue Publish Date: 01 Jan 2023

Abstract

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

FullText(HTML)

References(52)

References

[1]	Torres J J, Elices I, Marro J 2015 Plos One 10 e0121156 10.1371/journal.pone.0121156 doi: 10.1371/journal.pone.0121156
[2]	Torres J J, Marro J 2015 Sci. Rep. 5 12216 10.1038/srep12216 doi: 10.1038/srep12216
[3]	Guo D Q, Li C Q 2009 Phys. Rev.E 79 051921 10.1103/PhysRevE.79.051921 doi: 10.1103/PhysRevE.79.051921
[4]	Sun X J, Matjaz P, Lu Q S, Juergen K 2008 Chaos 18 023102 10.1063/1.2900402 doi: 10.1063/1.2900402
[5]	Yang X L, Jia Y B, Zhang L 2014 PhysicaA 393 617 10.1016/j.physa.2013.09.021 doi: 10.1016/j.physa.2013.09.021
[6]	Wang Q Y, Perc M, Duan Z S, Chen G R 2009 Chaos 19 023112 10.1063/1.3133126 doi: 10.1063/1.3133126
[7]	Wang Q Y, Zhang H H, Chen G R 2012 Chaos 22 043123 10.1063/1.4767719 doi: 10.1063/1.4767719
[8]	Liu G K, Quan H D, Kang Y M, Sun H X, Cui P Z, Han Y M 2019 Acta Phys. Sin. 68 210501 (in Chinese) 10.7498/aps doi: 10.7498/aps
[9]	Jin Y F 2018 Chin. Phys.B 27 050501 10.1088/1674-1056/27/5/050501 doi: 10.1088/1674-1056/27/5/050501
[10]	Uzuntarla M, Cressman J R, Ozer M, Barreto E 2013 Phys. Rev.E 88 042712 10.1103/PhysRevE.88.042712 doi: 10.1103/PhysRevE.88.042712
[11]	Torres J J, Uzuntarla M, Marro J 2020 Commun. Nonlinear Sci. Numer. Simulat. 80 104975 10.1016/j.cnsns.2019.104975 doi: 10.1016/j.cnsns.2019.104975
[12]	Zhu J J 2021 Chaos 31 033119 10.1063/5.0041410 doi: 10.1063/5.0041410
[13]	Yamakou M E, Jost J 2017 Europhys. Lett. 120 18002 10.1209/0295-5075/120/18002 doi: 10.1209/0295-5075/120/18002
[14]	Paydarfar D, Forger D B, Clay J R 2006 J. Neurophysiol 96 3338 10.1152/jn.00486.2006 doi: 10.1152/jn.00486.2006
[15]	Gutkin B S, Jost J, Tuckwell H C 2009 Naturwissenschaften 96 1091 10.1007/s00114-009-0570-5 doi: 10.1007/s00114-009-0570-5
[16]	Guo D Q 2011 Cogn. Neurodyn 5 293 10.1007/s11571-011-9160-2 doi: 10.1007/s11571-011-9160-2
[17]	Tuckwell H C, Jost J, Gutkin B S 2009 Phys. Rev.E 80 031907 10.1103/PhysRevE.80.031907 doi: 10.1103/PhysRevE.80.031907
[18]	Tuckwell H C, Jost J 2012 Phys.A 391 5311 10.1016/j.physa.2012.06.019 doi: 10.1016/j.physa.2012.06.019
[19]	Uzuntarla M 2013 Phys. Lett.A 377 2585 10.1016/j.physleta.2013.08.009 doi: 10.1016/j.physleta.2013.08.009
[20]	Uzuntarla M, Barreto E, Torres J J 2017 Plos Comput. Biol. 13 e1005646 10.1371/journal.pcbi.1005646 doi: 10.1371/journal.pcbi.1005646
[21]	Uzuntarla M, Torres J J, So P, Ozer M, Barreto E 2017 Phys. Rev.E 95 012404 10.1103/PhysRevE.95.012404 doi: 10.1103/PhysRevE.95.012404
[22]	Li D X, Cui X W, Yang Y C 2018 Neurocomputing 287 52 10.1016/j.neucom.2018.01.078 doi: 10.1016/j.neucom.2018.01.078
[23]	Zhao Y, Li D X 2019 Mod. Phys. Lett.B 33 1950252 10.1142/S021798491950252X doi: 10.1142/S021798491950252X
[24]	Lu L L, Jia Y, Ge M Y, Xu Y, Li A N 2020 Nonlinear Dyn. 100 877 10.1007/s11071-020-05492-y doi: 10.1007/s11071-020-05492-y
[25]	Li D X, Zhang N 2020 Chin. Phys.B 29 090201 10.1088/1674-1056/ab8c3f doi: 10.1088/1674-1056/ab8c3f
[26]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500 10.1113/jphysiol.1952.sp004764 doi: 10.1113/jphysiol.1952.sp004764
[27]	Fox R F 1997 Biophys Journal 72 2068 10.1016/S0006-3495(97)78850-7 doi: 10.1016/S0006-3495(97)78850-7
[28]	Gerstner W, Kistler W M 2002 Neural Comput. 14 987 10.1162/089976602753633358 doi: 10.1162/089976602753633358
[29]	Molz F J, Liu H H, Szulga J 1997 Water. Resour. Res. 33 2273 10.1029/97WR01982 doi: 10.1029/97WR01982
[30]	Mandelbrot B B, Van Ness J W 1968 SIAM. Rev. 10 422 10.1137/1010093 doi: 10.1137/1010093
[31]	Caraballo T, Garrido A M J, Taniguchi T 2011 Nonlinear. Anal. 74 3671 10.1016/j.na.2011.02.047 doi: 10.1016/j.na.2011.02.047
[32]	Duncan T E, Hu Y, Pasik-Duncan B 2000 SIAM Journal on Control and Optimization 38 582 10.1137/S036301299834171X doi: 10.1137/S036301299834171X
[33]	Mishura Y S 2008 Stochastic Calculus for Fractional Brownian Motion and Related Processes Berlin Heidelberg Springer-Verlag 10.1007/978-3-540-75873-0 doi: 10.1007/978-3-540-75873-0
[34]	Biagini F, Hu Y, Øksendal B, Zhang T 2008 Stochastic Calculus for Fractional Brownian Motion and Applications London Springer-Verlag Limited 10.1007/978-1-84628-797-8 doi: 10.1007/978-1-84628-797-8
[35]	Xu Y, Guo R, Liu D, Zhang H, Duan J 2014 Discrete Contin. Dynam. Systems (Series B) 19 1197 10.3934/dcdsb.2014.19.1197 doi: 10.3934/dcdsb.2014.19.1197
[36]	Delignières D 2015 Math. Probl. Eng. 2015 485623 10.1155/2015/485623 doi: 10.1155/2015/485623
[37]	Grigoriu M 2002 Applications in science and engineering Boston Birkhäuser 10.1007/978-0-8176-8228-6 doi: 10.1007/978-0-8176-8228-6
[38]	Hosking J R M 1984 Water resources research 20 1898 10.1029/WR020i012p01898 doi: 10.1029/WR020i012p01898
[39]	Asmussen S 1999 Notes of a Concentrated Advance Course at MaPhySto, Aarhus, Denmark
[40]	Lau W C, Erramilli A, Wang J L, Willinger W 1995 In Proceedings of ICC7#x2019;95
[41]	Kou S C, Xie X S 2004 Phys. Rev. Lett. 93 180603 10.1103/PhysRevLett.93.180603 doi: 10.1103/PhysRevLett.93.180603
[42]	Li M, Zhao W, Jia W, Long D, Chi C 2003 Appl. Math. Modelling 27 155 10.1016/S0307-904X(02)00087-2 doi: 10.1016/S0307-904X(02)00087-2
[43]	Paxson M 1997 Commun. Rev. 27 5
[44]	Dimakis A G, Maragos P 2004 IEEE Infocom. 27 877
[45]	Jones O, Shen Y 2004 IEEE Signal Proc. Lett. 11 416 10.1109/LSP.2004.824031 doi: 10.1109/LSP.2004.824031
[46]	Burnecki K, Weron A 2004 Acta Phys. Polon.B 35 1343
[47]	Xu Z, Gencay R 2003 Phys.A 323 578 10.1016/S0378-4371(03)00030-X doi: 10.1016/S0378-4371(03)00030-X
[48]	Kloeden P E, Platen E 1989 Stoch. Hydrol. Hydraul 3 155 10.1007/BF01543857 doi: 10.1007/BF01543857
[49]	Wang K K, Liu X B 2013 Chin. Phys. Lett. 30 070504 10.1088/0256-307X/30/7/070504 doi: 10.1088/0256-307X/30/7/070504
[50]	Dipoppa M, Gutkin B S 2013 Proc. Natl. Acad. Sci. USA 110 12828 10.1073/pnas.1303270110 doi: 10.1073/pnas.1303270110
[51]	Buchin A, Rieubland S, Häusser M, Gutkin B S, Roth A 2016 Plos Comput. Biol 12 1
[52]	Huh J H 2016 Phys. Rev.E 94 052702 10.1103/PhysRevE.94.052702 doi: 10.1103/PhysRevE.94.052702