禁忌学习神经元模型的电路设计及其动力学研究

陈军; 李春光

doi:10.7498/aps.60.020502

摘要

对禁忌学习混沌神经元模型进行了详细的电路设计,包括单神经元、具有线性相似函数的双神经元以及具有二次相似函数的双神经元模型,并运用EWB(Electronic Workbench)电路仿真软件对所设计的电路进行了仿真,研究了电路中的Hopf分叉和混沌等非线性动力学现象,通过与数值仿真结果的比对验证了所设计电路的正确性与合理性.

关键词:

The circuit design and implementation of neuron models have attracted much attention in recent years due to its importance in both theoretical studies and applications. In this paper, we designed electronic circuits for the recently proposed tabu learning chaotic neuron model, including the circuit design of single tabu learning neuron, a two-neuron system with linear proximity function, as well as a two-neuron system with quadratic proximity function. We used the electronic workbench (EWB) software to perform simulations of the designed circuits. We also studied the nonlinear behavior, especially the Hopf bifurcation and chaos, of the designed circuits. The consistency between the nonlinear behavior in the designed circuits and that in the numerical simulations demonstrates the correctness of the circuits design.

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)和全国优秀博士学位论文作者专项资金(批准号:2007B42)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

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[2]	Das II P K, Schieve W C, Zeng Z J 1991 Phys. Lett. A 161 60
[3]	Zou F, Nossek J A 1993 IEEE Trans. Circ. Sys. I 40 166
[4]	Li C G, Yu J B, Liao X F 2001 Phys. Lett. A 285 368
[5]	Das A, Das P, Roy A B 2002 Int.J. Bifurcat. Chaos 12 2271
[6]	Li C G, Chen G R, Liao X F, Yu J B 2004 Eur. Phys. J. B 41 337
[7]	Olien L, Belair J 1997 Phys. D 102 349
[8]	Lu H T 2002 Phys. Lett. A 298 109
[9]	Li C G, Liao X F, Yu J B 2003 Neurocomputing 55 731
[10]	Duan S K, Liao X F 2007 Phys. Lett. A 369 37
[11]	Kohno T, Aihara K 2005 IEEE Trans. on Neural Networks 16 754
[12]	Takemoto T, Kohno T, Aihara K 2007 Int. J. Bifurcat. Chaos 17 459
[13]	Beyer D A, Ogier R G 1991 Tabu Learning: A Neural Network Search Method for Solving Nonconvex Optimization Problems (Singapore: Proc. of the IJCNN) p953
[14]	Glover F 1989 ORSA J. Comput. 1 190
[15]	Glover F 1990 ORSA J. Comput. 2 4
[16]	Li C G, Chen G R, Liao X F, Yu J B 2005 Int. J. Bifurcat. Chaos 15 2633
[17]	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]
[18]	Conti M, Turchetti C 1994 IEEE Trans. Circuits Systems I 41 841
[19]	Carrasco-Robles M, Serrano L 2009 Int. J. Cir. Theor. Appl. 37 613
[20]	Liu L, Su Y C, Liu C X 2007 Acta Phys. Sin. 56 1966 (in Chinese) [刘凌、苏燕辰、刘崇新 2007 56 1966]
[21]	Liu C X 2007 Acta Phys. Sin. 56 6865 ( in Chinese) [刘崇新 2007 56 6865]
[22]	Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 56 3734]
[23]	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]
[24]	Tang L R, Li J, Fan B, Zhai M Y 2009 Acta Phys. Sin. 58 785 (in Chinese) [唐良瑞、李静、樊冰、翟明岳 2009 58 785]
[25]	Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese) [张若洵、杨世平2009 58 2957]
[26]	Cang S J, Chen Z Q, Wu W J 2009 Chin. Phys. B 18 1792
[27]	Zhou P, Cao Y X, Cheng X F 2009 Chin. Phys. B 18 1394
[28]	Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys. B 19 030509
[29]	Liu L, Su Y C, Liu C X 2006 Acta Phys. Sin. 55 3933 (in Chinese) [刘凌、苏燕辰、刘崇新 2006 55 3933]
[30]	Luo X H, Zhou W, Li R, Liang Y L, Lou M W 2009 Chin. Phys. B 18 2168
[31]	Ma W Q, Yang C H 2005 Acta Phys. Sin. 54 1064 (in Chinese) [马文麒、杨承辉 2005 54 1064]
[32]	Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振梅、周维怀、涂文桃 2007 56 6230]
[33]	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]
[34]	Chen J F, Tian X J, Shan J D 2010 Acta Phys.Sin. 59 2281 (in Chinese) [陈菊芳、田小建、单江东 2010 59 2281]
[35]	Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510

施引文献

[1]	Skarda C A, Freeman W J 1987 Behav. Brain Sci. 10 161
[2]	Das II P K, Schieve W C, Zeng Z J 1991 Phys. Lett. A 161 60
[3]	Zou F, Nossek J A 1993 IEEE Trans. Circ. Sys. I 40 166
[4]	Li C G, Yu J B, Liao X F 2001 Phys. Lett. A 285 368
[5]	Das A, Das P, Roy A B 2002 Int.J. Bifurcat. Chaos 12 2271
[6]	Li C G, Chen G R, Liao X F, Yu J B 2004 Eur. Phys. J. B 41 337
[7]	Olien L, Belair J 1997 Phys. D 102 349
[8]	Lu H T 2002 Phys. Lett. A 298 109
[9]	Li C G, Liao X F, Yu J B 2003 Neurocomputing 55 731
[10]	Duan S K, Liao X F 2007 Phys. Lett. A 369 37
[11]	Kohno T, Aihara K 2005 IEEE Trans. on Neural Networks 16 754
[12]	Takemoto T, Kohno T, Aihara K 2007 Int. J. Bifurcat. Chaos 17 459
[13]	Beyer D A, Ogier R G 1991 Tabu Learning: A Neural Network Search Method for Solving Nonconvex Optimization Problems (Singapore: Proc. of the IJCNN) p953
[14]	Glover F 1989 ORSA J. Comput. 1 190
[15]	Glover F 1990 ORSA J. Comput. 2 4
[16]	Li C G, Chen G R, Liao X F, Yu J B 2005 Int. J. Bifurcat. Chaos 15 2633
[17]	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]
[18]	Conti M, Turchetti C 1994 IEEE Trans. Circuits Systems I 41 841
[19]	Carrasco-Robles M, Serrano L 2009 Int. J. Cir. Theor. Appl. 37 613
[20]	Liu L, Su Y C, Liu C X 2007 Acta Phys. Sin. 56 1966 (in Chinese) [刘凌、苏燕辰、刘崇新 2007 56 1966]
[21]	Liu C X 2007 Acta Phys. Sin. 56 6865 ( in Chinese) [刘崇新 2007 56 6865]
[22]	Hu G S 2009 Acta Phys. Sin. 58 3734 (in Chinese) [胡国四 2009 56 3734]
[23]	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]
[24]	Tang L R, Li J, Fan B, Zhai M Y 2009 Acta Phys. Sin. 58 785 (in Chinese) [唐良瑞、李静、樊冰、翟明岳 2009 58 785]
[25]	Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese) [张若洵、杨世平2009 58 2957]
[26]	Cang S J, Chen Z Q, Wu W J 2009 Chin. Phys. B 18 1792
[27]	Zhou P, Cao Y X, Cheng X F 2009 Chin. Phys. B 18 1394
[28]	Wang H X, Cai G L, Miao S, Tian L X 2010 Chin. Phys. B 19 030509
[29]	Liu L, Su Y C, Liu C X 2006 Acta Phys. Sin. 55 3933 (in Chinese) [刘凌、苏燕辰、刘崇新 2006 55 3933]
[30]	Luo X H, Zhou W, Li R, Liang Y L, Lou M W 2009 Chin. Phys. B 18 2168
[31]	Ma W Q, Yang C H 2005 Acta Phys. Sin. 54 1064 (in Chinese) [马文麒、杨承辉 2005 54 1064]
[32]	Cai G L, Tan Z M, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振梅、周维怀、涂文桃 2007 56 6230]
[33]	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]
[34]	Chen J F, Tian X J, Shan J D 2010 Acta Phys.Sin. 59 2281 (in Chinese) [陈菊芳、田小建、单江东 2010 59 2281]
[35]	Zhang R X, Yang S P 2010 Chin. Phys. B 19 020510

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