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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.
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Keywords:
- nonlinear circuit /
- chaos /
- integrate-and-discharge model /
- symbolic dynamics
[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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[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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