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

[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

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

[1]	刘昊华, 王少华, 李波波, 李桦林. 缺陷致非线性电路孤子非对称传输. , 2017, 66(10): 100502. doi: 10.7498/aps.66.100502
[2]	徐红梅, 金永镐, 金璟璇. 基于符号动力学的开关变换器时间不可逆性分析. , 2014, 63(13): 130502. doi: 10.7498/aps.63.130502
[3]	王光义, 袁方. 级联混沌及其动力学特性研究. , 2013, 62(2): 020506. doi: 10.7498/aps.62.020506
[4]	肖建新, 陈菊芳, 彭建华. 一个简单延迟非线性系统的动力学行为及混沌同步. , 2013, 62(17): 170507. doi: 10.7498/aps.62.170507
[5]	余洋, 米增强. 机械弹性储能机组储能过程非线性动力学模型与混沌特性. , 2013, 62(3): 038403. doi: 10.7498/aps.62.038403
[6]	李群宏, 闫玉龙, 杨丹. 耦合电路系统的分岔研究. , 2012, 61(20): 200505. doi: 10.7498/aps.61.200505
[7]	宋爱玲, 黄晓林, 司峻峰, 宁新宝. 符号动力学在心率变异性分析中的参数选择. , 2011, 60(2): 020509. doi: 10.7498/aps.60.020509
[8]	陈军, 李春光. 具有自适应反馈突触的神经元模型中的混沌:电路设计. , 2011, 60(5): 050503. doi: 10.7498/aps.60.050503
[9]	古华光, 朱洲, 贾冰. 一类新的混沌神经放电的动力学特征的实验和数学模型研究. , 2011, 60(10): 100505. doi: 10.7498/aps.60.100505
[10]	张银, 毕勤胜. 具有多分界面的非线性电路中的非光滑分岔. , 2011, 60(7): 070507. doi: 10.7498/aps.60.070507
[11]	王福来. 基于复合符号混沌的伪随机数生成器及加密技术. , 2011, 60(11): 110517. doi: 10.7498/aps.60.110517
[12]	张晓芳, 陈章耀, 毕勤胜. 非线性电路通向混沌的演化过程. , 2010, 59(5): 3057-3065. doi: 10.7498/aps.59.3057
[13]	沈民奋, 林兰馨, 李小艳, 常春起. 基于符号动力学的耦合映像格子系统的初值估计. , 2009, 58(5): 2921-2929. doi: 10.7498/aps.58.2921
[14]	张晓芳, 陈章耀, 毕勤胜. 耦合电路中的复杂振荡行为分析. , 2009, 58(5): 2963-2970. doi: 10.7498/aps.58.2963
[15]	刘小峰, 俞文莉. 基于符号动力学的认知事件相关电位的复杂度分析. , 2008, 57(4): 2587-2594. doi: 10.7498/aps.57.2587
[16]	时培明, 刘彬, 侯东晓. 一类相对转动非线性动力系统的混沌运动. , 2008, 57(3): 1321-1328. doi: 10.7498/aps.57.1321
[17]	王开, 裴文江, 夏海山, 何振亚. 基于符号向量动力学的耦合映像格子初始向量估计. , 2007, 56(7): 3766-3770. doi: 10.7498/aps.56.3766
[18]	于洪洁, 刘延柱. 对称非线性耦合混沌系统的同步. , 2005, 54(7): 3029-3033. doi: 10.7498/aps.54.3029
[19]	肖方红, 阎桂荣, 韩宇航. 混沌伪随机序列复杂度分析的符号动力学方法. , 2004, 53(9): 2876-2881. doi: 10.7498/aps.53.2876
[20]	伍维根, 古天祥. 混沌系统的非线性反馈跟踪控制. , 2000, 49(10): 1922-1925. doi: 10.7498/aps.49.1922

计量

文章访问数: 6446
PDF下载量: 498
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板