摘要
本文首先简单介绍了随机共振和随机自共振的概念、物理意义、理论模型和实验验证。在此基础上。着重对高度非线性的神经系统电活动的随机共振现象进行了介绍。内容包括神经元动力系统的非线性、神经元随机共振、随机自共振的实验和理论解释。
参考文献21
-
1Benzi R, Sutera S. Vulpiani A. The Mechanism of Stochastic Resonance. l Phys A, 1981, 14:LA53-LA57.
-
2Fauve S. Heslot E Stochastic Resonance in a Bistable System. Phys Lett A, 1983.97:5-7.
-
3Hu G, Ditzinger T. Ning C.Z. Stochastic Resonance Without External Periodic Force. Phys Rev Lett, 1993, 71 :807-810.
-
4Hart K, Yim T G, Postnov D E, et al. Interacting Coherence Resonance Oscillators. Phys Rev Lett, 1999,83(9): 1771 - 1774.
-
5Ren W, Hu S J, B J Zhang, et al. Period-Adding Bifurcation with Chaos in the Interspike Intervals Generated by an-Experimental Neural Pacemaker. Int J Bifur Chaos, 1997,7:1867-1872.
-
6(3u H G, Ren W, Lu Q S, Wu S G, Yang M H, Chen W J. Integer Multiple Spiking in the Neuronal Pacemaker Without External Stimulation. Phys Lett A, 2001, 285:63-68.
-
7Braun H A, Wissing H, Schafer K, et al. Oscillation and Noise Determine Signal Transduction in Shark Multimodal Sensory Cells. Nature, 1994, 367:270-273.
-
8Rose J E, Bmgge J F, Arderson D D, Hind J E. Phase-Locked Response to Low-Frequency Tones in Single Auditory Nerve Fibers of the Squirrel Monkey. J Neurophysiol, 1967, 30:769.
-
9Siegel R M. Nonlinear Dynamical System Theory and Primary Visual Conical Processing. Phys D, 1990,42:385-395.
-
10Longtin A, Bulsara A, Moss F, et al. Tune Interval Sequences in Bistable System and Ihe Noise-Induced Transmission of Information by Sensory Neurons. Phys Rev Lett, 1991, 67:656,-659.
同被引文献11
-
1王江,耿建明,费向阳.HHM模型的多参数Hopf分岔分析[J].系统仿真学报,2005,17(1):170-173. 被引量:1
-
2张广军,徐健学.非线性动力系统分岔点邻域内随机共振的特性[J].物理学报,2005,54(2):557-564. 被引量:21
-
3官山,陆启韶.odgkin—Huxley方程的Hopf分岔的研究[J].非线性动力学学报,1996,3(3):252-257. 被引量:1
-
4Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. Physiol, 1952; 117 : 500.
-
5Fitzhugh R. Impulse and physiological states in theoretical models of nerve membrene. Biophys, 1961 ; 1:445.
-
6Rinzel J. One repetitive activity in nerve. Fed Proc, 1978; 37 : 2793.
-
7Troy WC. The bifurcation in the Hoclgldn-Huxley equations. Appl Math, 1978;6:73.
-
8Bedrov YA, Akoev GN,Dick OE. On the relationship between the number of negative slope regions in the voltage-current curve of the Hodgkin Huxley model and its parameter values. Biol Cybern, 1995; 73 : 149.
-
9唐文亮.神经脉冲传导的一种解与动作势的稳定性[J].应用数学和力学,1983,4(1):113-113.
-
10Chert ZX, Guo BY. Long-time behaviour of the partially uniform discrete Nagumo model. Mathematical Methods in the Applied Sciences, 1993; 16 : 305.
二级引证文献4
-
1李向正,张卫国,原三领.神经脉冲传播的一种特殊模型的研究[J].生物医学工程学杂志,2010,27(5):1142-1145. 被引量:3
-
2林府标,张千宏,张俊,龙文.预李群分类法的应用和Fitzhugh-Nagumo方程的行波解[J].应用数学,2017,30(4):908-915. 被引量:7
-
3朱立贤,田福泽,董群喜,赵庆林,何安平,郑炜豪,胡斌.基于异步芯片的多模态神经生理信号采集技术[J].数据采集与处理,2022,37(4):848-859. 被引量:3
-
4杨洁,肖冰.KdV方程在神经细胞脉冲传导的孤立子性质[J].理论数学,2019,9(10):1159-1166.
-
1李玉叶,王晓英.亚临界Hopf分岔附近的随机自共振[J].廊坊师范学院学报(自然科学版),2015,15(2):11-13.
-
2古华光,任维,陆启韶,杨明浩.实验性神经起步点自发放电的分叉和整数倍节律[J].生物物理学报,2001,17(4):637-644. 被引量:16
-
3睡眠大脑的不连通性[J].生物学通报,2005,40(11):11-11.
-
4李玉叶,王晓英.亚临界Hopf分岔附近的神经放电的随机节律[J].赤峰学院学报(自然科学版),2014,30(11):1-2. 被引量:1
-
5古华光,任维,杨明浩,李莉,刘志强.神经自发整数倍峰放电节律的随机性和确定性模式的比较[J].生物物理学报,2003,19(3):272-278. 被引量:8
-
6古华光,任维.感觉神经放电中的随机共振现象和噪声的作用[J].生理科学进展,2004,35(4):364-367. 被引量:1
-
7任维,陆启韶,等.实验性神经起步点自发放电的整数倍节律和随机自共振[J].非线性动力学学报,2001,8(2):106-112.
-
8林冬翠.扰动条件下Hodgkin-Huxley神经元模型方程的数值解法[J].广西教育,2013(19):152-153.
-
9李玉叶.随机因素作用下的超临界Hopf分岔附近的动力学[J].赤峰学院学报(自然科学版),2014,30(13):3-6.
-
10杨明浩,古华光,李莉,刘志强,任维.神经放电加周期分岔中由随机自共振引起一类新节律[J].生物物理学报,2004,20(6):465-470. 被引量:6