累积放电模型及其符号动力学研究

陈冲; 丁炯; 张宏; 陈琢

doi:10.7498/aps.62.140502

摘要

基于累积释放模型提出了一种累积放电模型.相比于累积释放模型, 累积放电模型无须变化的阈值调制, 即可出现多种状态, 例如混沌态、锁频等. 利用符号动力学对其进行研究, 发现在一定的参数条件下, 模型的输出符号序列可以被用于监测模型参数的变化, 而且与神经系统的测量相似, 都具有很高的分辨率. 计算机仿真和电路实验得到的结果也验证了上述说法. 电路实验结果显示模型的输出符号序列对输入频率的分辨率最高可以达到0.05 Hz, 对电流幅值的分辨率可达到1 μA, 并且都具有很大的动态范围.

关键词:

Abstract

An integrate-and-discharge model (IDM) is proposed on the basis of an integrate-and-fire model (IFM). Compared with the IFM, the IDM can obtain rich dynamic information including chaos, phase locking, etc., without using varying threshold modulation. The corresponding relation between output symbolic sequences and parameters (i.e., frequency, amplitude, resistance and capacity) of the IDM is established by using symbolic dynamics. Moreover, a method of obtaining symbolic sequence as well as an ordering rule is presented. Simulation and circuit experiment validate the correctness of the method and the rule. The results of circuit experiment show that the frequency resolution can reach up to 0.05 Hz in some frequency ranges and the amplitude resolution can reach up to 1 μA.

Keywords:

作者及机构信息

1.
浙江大学生物医学工程系, 杭州 310027;

2.
浙江大学城市学院自动化系, 杭州 310015

基金项目: 国家自然科学基金(批准号: 60871085)和浙江省自然科学基金(批准号: Y1100119)资助的课题.

Authors and contacts

1.
Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China;

2.
Department of Automation, Zhejiang University City College, Hangzhou 310015, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60871085) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y1100119).

参考文献

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[3]	Meucci R, Euzzor S, Geltrude A, Al-Naimee K, De Nicola S, Arecchi F T 2012 Phys. Lett. A 376 834
[4]	Zhang J J, Jin Y F 2012 Acta Phys. Sin. 61 130502 (in Chinese) [张静静, 靳艳飞 2012 61 130502]
[5]	Brette R 2004 J. Math. Bio. 48 38
[6]	Hertag L, Hass J, Golovko T, Durstewitz D 2012 Front. Comput. Neurosci. 6 62
[7]	Koch C 1999 Biophysics of Computation (New York: New York Oxford University Press) pp11-13
[8]	Hamanaka H, Torikai H, Saito T 2006 Circuits and Systems I!I: Express Briefs, IEEE Transactions on 53 1049
[9]	Ott E 1993 Chaos in Dynamical Systems (New York: Cambridge University Press) pp6-44
[10]	Saito T, Kabe T, Ishikawa Y, Matsuoka Y, Torikai H 2007 Int. J. Bifurcat. Chaos 17 3373
[11]	Zhou D, Sun Y, Rangan A V, Cai D 2010 J. Comput. Neurosci. 28 229
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[13]	Zhou G H, Xu J P, Bao B C, Zhang F, Liu X S 2010 Chin. Phys. Lett. 27 090504
[14]	Zheng W M, Hao B L 1990 Applied Symbolic Dynamics, in Experimental Study and Characterization of Chaos (Singapore: World Scientific) pp363-459
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施引文献

[1]	Buhry L, Grassia F, Giremus A, Grivel E, Renaud S, Saighi S 2011 Neural Comput. 23 2599
[2]	Ding J, Zhang H, Tong Q Y 2012 Acta Phys. Sin. 61 150505 (in Chinese) [丁炯, 张宏, 童勤业 2012 61 150505]
[3]	Meucci R, Euzzor S, Geltrude A, Al-Naimee K, De Nicola S, Arecchi F T 2012 Phys. Lett. A 376 834
[4]	Zhang J J, Jin Y F 2012 Acta Phys. Sin. 61 130502 (in Chinese) [张静静, 靳艳飞 2012 61 130502]
[5]	Brette R 2004 J. Math. Bio. 48 38
[6]	Hertag L, Hass J, Golovko T, Durstewitz D 2012 Front. Comput. Neurosci. 6 62
[7]	Koch C 1999 Biophysics of Computation (New York: New York Oxford University Press) pp11-13
[8]	Hamanaka H, Torikai H, Saito T 2006 Circuits and Systems I!I: Express Briefs, IEEE Transactions on 53 1049
[9]	Ott E 1993 Chaos in Dynamical Systems (New York: Cambridge University Press) pp6-44
[10]	Saito T, Kabe T, Ishikawa Y, Matsuoka Y, Torikai H 2007 Int. J. Bifurcat. Chaos 17 3373
[11]	Zhou D, Sun Y, Rangan A V, Cai D 2010 J. Comput. Neurosci. 28 229
[12]	Hao B L 1993 Starting with Parabolas: An Introduction to Chaotic Dynamics (Shanghai: Shanghai Science and Technology Education Press) p123 (in Chinese) [郝柏林 1993 从抛物线谈起-混沌动力学引论(上海: 上海科技教育出版社) 第123页]
[13]	Zhou G H, Xu J P, Bao B C, Zhang F, Liu X S 2010 Chin. Phys. Lett. 27 090504
[14]	Zheng W M, Hao B L 1990 Applied Symbolic Dynamics, in Experimental Study and Characterization of Chaos (Singapore: World Scientific) pp363-459
[15]	Brown R, Chua L 1992 Int. J. Bifurcat. Chaos 2 193
[16]	Huang W G, Tong Q Y 2002 J. Electron. Informat. Technol. 24 6 (in Chinese) [黄文高, 童勤业 2002电子与信息学报 24 6]
[17]	Zhang Z J, Chen S G 1989 Acta Phys. Sin. 38 8 (in Chinese) [张忠建, 陈式刚 1989 38 8]
[18]	Kohda T, Horio Y, Takahashi Y, Aihara K 2012 Int. J. Bifurcat. Chaos 22 1230031

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