具有自适应反馈突触的神经元模型中的混沌:电路设计

陈军; 李春光

doi:10.7498/aps.60.050503

摘要

近期文献中报道了在具有自适应反馈突触的神经元模型中,随着参数的变化,存在从两个共存吸引子到一个相连吸引子再到两个共存吸引子的混沌转化现象.本文对此模型进行了电路设计,同时对具有非单调激活函数功能的电路设计进行了细致的研究,并利用Electronic Workbench (EWB)软件对所设计的电路进行了仿真实验,研究了电路中的混沌现象,验证了所设计电路的动力学行为与通过数值模拟结果十分相似.

关键词:

In a neuron model with adaptive feedback synapse, with the change of parameters, the existence of two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor,and then switching back to the two coexisting chaotic attractors in this model were recently reported. An electronic circuit design for this model is described in detail in this paper. The circuit design of the non-monotonous activation function unit is also considered in detail. The designed circuits are simulated using the Electronic Workbench (EWB) software. Simulation results demonstrate that the dynamical behaviors of the designed circuit are closely similar to those in numerical simulations.

Keywords:

作者及机构信息

陈军¹,
李春光²

(1)定西师范高等专科学校物理与电子工程学系,定西 743000;浙江大学信息与电子工程学系,杭州 310027; (2)浙江大学信息与电子工程学系,杭州 310027

基金项目: 国家自然科学基金(批准号:60871094),全国优秀博士学位论文作者专项资金(批准号:2007B42 )和中央高校基本科研业务费专项资金(批准号:2009QNA5026,2010QNA5031)资助的课题.

Authors and contacts

Li Chun-Guang¹,
Chen Jun²

(1)Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China; (2)Department of Physics and Electronic Engineering, Dingxi Teachers’ College, Dingxi 743000, China; Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China

参考文献

[1]	Tao C H, Lu J A, Lü J H 2002 Acta Phys. sin. 51 1497 (in Chinese)[陶朝海、陆君安、吕金虎 2002 51 1497]
[2]	Li C G, Chen G R 2005 Chaos, Solitons and Fractals 23 1599
[3]	Kürten K E, Clark J W 1986 Phys. Let. A 114 413
[4]	Zou F, Nossek J A 1993 IEEE Trans. CSA-I 40 166
[5]	Li C G, Yu J B, Liao X F 2001 Phys. Lett. A 285 368
[6]	Li C G, Chen G R, Liao X F 2005 Int. J. Bifur. Chaos 15 2633
[7]	Bondarenko V E 1997 Phys. Lett. A 236 513
[8]	Li C G, Chen G R, Liao X F, Yu J B 2004 Eur. Phys. J. B 41 337
[9]	Liao X F, Wong K W, Leung C S, Wu Z F 2001 Chaos, Solitons and Fractals 12 1535
[10]	Gilli M 1993 IEEE Trans. CAS-I 40 849
[11]	Lu H T 2002 Phys. lett. A 298 109
[12]	Wheeler D W, Schieve W C 1997 Phys. D 105 267
[13]	Chen L N, Aihara K 1995 Neural Networks8 915
[14]	Chen L N, Aihara K 2001 IEEE Trans. CAS-I 47 1455
[15]	Li C G, Liao X F, Yu J B 2003 Neurocomputing 55 731
[16]	Wang Q Y, Lu Q S, Wang H X 2005 Chin. Phys. 14 2189
[17]	Wang Q Y, Lu Q S, Chen G R 2008 Int. J. Bifur. Chaos 18 1189
[18]	Duan S K, Liao X F 2007 Phys. Lett. A 369 37
[19]	Duan S K, Wang L D 2009 Computers & Mathematics with Applications 57 1736
[20]	Sekikawa M, Kohno T, Aihara K 2008 Artif Life and Robotics 13 116
[21]	Takemoto T, Kohno T, Aihara K 2007 Int. J. Bifur. Chaos 17 459
[22]	Chen J, Li C G 2011 Acta Phys. Sin. 60 020502 (in Chinese) [陈军、李春光 2011 60 020502]
[23]	Caroppo D, Stramaglia S 1998 Phys. Lett. A 246 55
[24]	Dror G, Tsodyks M 2000 Neurocomputing 32-33 365
[25]	Dong D W, Hopfield J J 1992 Network: Comp Neural Sys. 3 267
[26]	Wang G H 2008 Circuit designing and its application of Multisim 10 (Beijing: National Defense Industry Publishing House) p122 (in Chinese) [王冠华2008 Multisim10电路设计及应用 (北京:国防工业出版社) 第122页]
[27]	Jia H Y, Chen Z Q, Yuan Z Z 2009 Acta Phys. Sin. 58 4469 (in Chinese) [贾红艳、陈增强、袁著祉 2009 58 4469]
[28]	Liu L, Su Y Z, Liu C X 2007 Acta Phys. Sin. 56 1966 ( in Chinese) [刘凌、苏燕辰、刘崇新 2007 56 1966]
[29]	Cang S J, Chen Z Q, Wu W J 2009 Chin. Phys. B 18 1792
[30]	Chen Z Y, Zhang X F, Bi Q S 2010 Acta Phys. Sin. 59 2326 (in Chinese) [陈章耀、张晓芳、毕勤胜 2010 59 2326]
[31]	Liu C X 2007 Acta Phys. Sin. 56 6865 ( in Chinese) [刘崇新 2007 56 6865]
[32]	Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[33]	Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys. B 19 030509

施引文献

[1]	Tao C H, Lu J A, Lü J H 2002 Acta Phys. sin. 51 1497 (in Chinese)[陶朝海、陆君安、吕金虎 2002 51 1497]
[2]	Li C G, Chen G R 2005 Chaos, Solitons and Fractals 23 1599
[3]	Kürten K E, Clark J W 1986 Phys. Let. A 114 413
[4]	Zou F, Nossek J A 1993 IEEE Trans. CSA-I 40 166
[5]	Li C G, Yu J B, Liao X F 2001 Phys. Lett. A 285 368
[6]	Li C G, Chen G R, Liao X F 2005 Int. J. Bifur. Chaos 15 2633
[7]	Bondarenko V E 1997 Phys. Lett. A 236 513
[8]	Li C G, Chen G R, Liao X F, Yu J B 2004 Eur. Phys. J. B 41 337
[9]	Liao X F, Wong K W, Leung C S, Wu Z F 2001 Chaos, Solitons and Fractals 12 1535
[10]	Gilli M 1993 IEEE Trans. CAS-I 40 849
[11]	Lu H T 2002 Phys. lett. A 298 109
[12]	Wheeler D W, Schieve W C 1997 Phys. D 105 267
[13]	Chen L N, Aihara K 1995 Neural Networks8 915
[14]	Chen L N, Aihara K 2001 IEEE Trans. CAS-I 47 1455
[15]	Li C G, Liao X F, Yu J B 2003 Neurocomputing 55 731
[16]	Wang Q Y, Lu Q S, Wang H X 2005 Chin. Phys. 14 2189
[17]	Wang Q Y, Lu Q S, Chen G R 2008 Int. J. Bifur. Chaos 18 1189
[18]	Duan S K, Liao X F 2007 Phys. Lett. A 369 37
[19]	Duan S K, Wang L D 2009 Computers & Mathematics with Applications 57 1736
[20]	Sekikawa M, Kohno T, Aihara K 2008 Artif Life and Robotics 13 116
[21]	Takemoto T, Kohno T, Aihara K 2007 Int. J. Bifur. Chaos 17 459
[22]	Chen J, Li C G 2011 Acta Phys. Sin. 60 020502 (in Chinese) [陈军、李春光 2011 60 020502]
[23]	Caroppo D, Stramaglia S 1998 Phys. Lett. A 246 55
[24]	Dror G, Tsodyks M 2000 Neurocomputing 32-33 365
[25]	Dong D W, Hopfield J J 1992 Network: Comp Neural Sys. 3 267
[26]	Wang G H 2008 Circuit designing and its application of Multisim 10 (Beijing: National Defense Industry Publishing House) p122 (in Chinese) [王冠华2008 Multisim10电路设计及应用 (北京:国防工业出版社) 第122页]
[27]	Jia H Y, Chen Z Q, Yuan Z Z 2009 Acta Phys. Sin. 58 4469 (in Chinese) [贾红艳、陈增强、袁著祉 2009 58 4469]
[28]	Liu L, Su Y Z, Liu C X 2007 Acta Phys. Sin. 56 1966 ( in Chinese) [刘凌、苏燕辰、刘崇新 2007 56 1966]
[29]	Cang S J, Chen Z Q, Wu W J 2009 Chin. Phys. B 18 1792
[30]	Chen Z Y, Zhang X F, Bi Q S 2010 Acta Phys. Sin. 59 2326 (in Chinese) [陈章耀、张晓芳、毕勤胜 2010 59 2326]
[31]	Liu C X 2007 Acta Phys. Sin. 56 6865 ( in Chinese) [刘崇新 2007 56 6865]
[32]	Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510
[33]	Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys. B 19 030509

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