Neuromorphic behaviors of N-type locally-active memristor

Wang Shi-Chang; Lu Zhen-Zhou; Liang Yan; Wang Guang-Yi

doi:10.7498/aps.71.20212017

Abstract

Owing to the advantages of high integration, low power consumption and locally active characteristics, locally-active memristor (LAM) has shown great potential applications in neuromorphic computing. To further investigate the neuromorphic dynamics of LAMs, a simple N-type LAM mathematical model is proposed in this work. By analyzing its voltage-current characteristic and small-signal equivalent circuit, a neuron circuit based on the N-type LAM is designed, where a variety of neuromorphic behaviors are successfully simulated, such as “all-or-nothing” behavior, spikes, bursting, periodic oscillation, etc. Moreover, Hopf bifurcation theory and numerical analysis method are used to study the dynamics of the circuit quantitatively. Then, an artificial tactile neuron and its frequency characteristics are presented by using the proposed neuron circuit topology. The simulation results show that when the amplitude of the input signal is lower than the threshold, the oscillation frequency of the output signal of the artificial neuron circuit is positively correlated with the intensity of the input signal, and reaches a maximum value at the threshold. The above frequency characteristics are consistent with those of the exciting state of biological sensory system. Subsequently, if the incentive intensity continues to increase, the oscillation frequency will gradually decrease, corresponding to the protective inhibition behavior. Finally, the physical circuit of the N-type LAM, and artificialneuron circuit are realized. The experimental results accord well with the simulation results and theoreticalanalyses, manifesting the practicability of the N-type LAM model and the feasibility of artificial neuron circuit.

Keywords:

Authors and contacts

School of Electronic Information, Hangzhou Dianzi University, Hangzhou 310018, China

Corresponding author: Lu Zhen-Zhou, luzhz@hdu.edu.cn

Funds: Project supported by the Natural Science Foundation of Zhejiang Pvovince, China (Grant No. LY20F010008) and the National Natural Science Foundation of China (Grant No. 62171173)

FullText HTML : translate this paragraph

References

[1]	Moore G E 1998 Proc. IEEE 86 82 Google Scholar
[2]	Backus J 1978 Commun. ACM. 21 613 Google Scholar
[3]	Zhao Y, Liu B, Yang J, He J, Jiang J 2020 Chin. Phys. Lett. 37 088501 Google Scholar
[4]	Chen Y-B, Yang X-K, Yan T, Wei B, Cui H-Q, Li C, Cai L 2020 Chin. Phys. Lett. 37 078501 Google Scholar
[5]	Kumar S, Williams R S, Wang Z 2020 Nature 585 518
[6]	Maass W 1997 Neural. Netw. 10 659 Google Scholar
[7]	Merolla P A, Arthur J V, Alvarez-Icaza R, et al. 2014 Science 345 668 Google Scholar
[8]	Davies M, Srinivasa N, Lin T H, et al. 2018 IEEE Micro. 38 82 Google Scholar
[9]	Indiveri G, Linares-Barranco B, Hamilton T J, et al. 2011 Front. Neurosci. 5 73 Google Scholar
[10]	Kim H, Hwang S, Park J, Yun S, Lee J H, Park B G 2018 IEEE Electron. Device Lett. 39 630 Google Scholar
[11]	Wang W, Pedretti G, Milo V, Carboni R, Calderoni A, Ramaswamy N, Spinelli A S, Ielmini D 2018 Sci. Adv. 4 eaat4752 Google Scholar
[12]	Prezioso M, Mahmoodi M R, Bayat F M, Nili H, Kim H, Vincent A, Strukov D B 2018 Nat. Commun. 9 5311 Google Scholar
[13]	Wang Z, Joshi S, Savel’ev S, et al. 2018 Nat. Electron. 1 137 Google Scholar
[14]	Roy K, Jaiswal A, Panda P 2019 Nature 575 607 Google Scholar
[15]	Wang M, Cai S, Pan C, Wang C, Lian X, Zhuo Y, Xu K, Cao T, Pan X, Wang B, Liang S J, Yang J J, Wang P, Miao F 2018 Nat. Electron. 1 130 Google Scholar
[16]	Pickett M D, Williams R S 2012 Nanotechnology 23 215202 Google Scholar
[17]	Choi S, Tan S H., Li Z, Kim Y, Choi C, Chen P Y, Yeon H, Yu S, Kim J 2018 Nat. Mater. 17 335 Google Scholar
[18]	Li C, Hu M, Li Y, et al. 2018 Nat. Electron. 1 52 Google Scholar
[19]	Hu M, Graves C E, Li C, Li Y, Ge N, Montgomery E, Davila N, Jiang H, Williams R S, Yang J J, Xia Q, Strachan J P 2018 Adv. Mater. 30 1705914 Google Scholar
[20]	Valov I, Linn E, Tappertzhofen S, Schmelzer S, van den Hurk J, Lentz F, Waser R 2013 Nat. Commun. 4 1771 Google Scholar
[21]	Wang Z, Rao M, Han J W, et al. 2018 Nat. Commun. 9 3208 Google Scholar
[22]	Yang Y, Gao P, Li L, Pan X, Tappertzhofen S, Choi S, Waser R, valov I, Lu W D. 2014 Nat. Commun. 5 4232 Google Scholar
[23]	Liang Y, Wang G, Chen G, Dong Y, Yu D, Iu H H C 2020 IEEE Trans. Circuits. Syst. I. Regul. Pap. 67 5139 Google Scholar
[24]	Li C, Wang Z, Rao M, Belkin D, Song W, Jiang H, Yan P, Li Y, Lin P, Hu M, Ge N, Stranchan J P, Barnell M, Wu Q, Williams R S, Yang J J, Xia Q 2019 Nat. Mach. Intell. 1 49 Google Scholar
[25]	Li C, Belkin D, Li Y, Yan P, Hu M, Ge N, Jiang H, Montgomery E, Lin P, Wang Z, Song W, Strachan J P, Barnell M, Wu Q, Williams R S, Yang J J, Xia Q 2018 Nat. Commun. 9 2385 Google Scholar
[26]	Zhang C, Chen Y, Yi M, Zhu Y, Li T, Liu L, Wang L, Xie L, Huang W 2018 Sci. Sin. Inform. 48 115 Google Scholar
[27]	Chua L O 2005 Int. J. Bifurcat. Chaos. 15 3435 Google Scholar
[28]	Mainzer K, Chua L O 2013 Local Activity Principle (London: Imperial College Press)
[29]	Midya R, Wang Z, Asapu S, Joshi S, Li Y, Zhuo Y, Song W, Jiang H, Upadhay N, Rao M, Lin P, Li C, Xia Q, Yang J J 2019 Adv. Electron. Mater. 5 1900060 Google Scholar
[30]	Zhu J, Wu Z, Zhang X, Wang Y, Lu J, Chen P, Cheng L, Shi T, Liu Q 2021 5th IEEE Electron Devices Technology & Manufacturing Conference Chengdu, China, March 9–12, 2021 pp1–3
[31]	Al-Shedivat M, Naous R, Cauwenberghs G, Salama K N 2015 IEEE J. Emerg. Sel. Topic. Power Electon. 5 242 Google Scholar
[32]	Zhang X, Zhuo Y, Luo Q, Wu Z, Midya R, Wang Z, Song W, Wang R, Upadhyay N K, Fang Y, Kiani F, Rao M, Yang Y, Xia Q, Liu Q, Liu M, Yang J J 2020 Nat. Commun. 11 51 Google Scholar
[33]	Chua L O 2011 Appl. Phys. A 102 765 Google Scholar
[34]	Liang Y, Lu Z, Wang G, Dong Y, Yu D, Iu H H C 2020 IEEE Access 8 75571 Google Scholar

Cited By

图 1 N型LAM不同频率下的捏滞回环曲线

Figure 1. Pinch hysteresis loop curves of the N-type LAM under different frequencies.

DownLoad: Full-Size Img PowerPoint

图 2 N型LAM电学特性曲线

Figure 2. N-type LAM electrical characteristic curves.

DownLoad: Full-Size Img PowerPoint

图 3 N型LAM小信号等效电路

Figure 3. N-type LAM small-signal equivalent circuit.

DownLoad: Full-Size Img PowerPoint

图 4 基于N型LAM的神经元电路

Figure 4. Neuron circuit based on the N-type LAM.

DownLoad: Full-Size Img PowerPoint

图 5 (a) 在V_D = 3 V且30 mH ≤ L ≤ 600 mH范围下, 雅可比矩阵特征值的轨迹; (b) 逐步增大电感, 人工神经元电路可振荡条件下, V_D范围变化趋势

Figure 5. (a) The trajectory of the Jacobian matrix eigenvalues with V_D = 3 V and 30 mH ≤ L ≤ 600 mH; (b) with the artificial neuron circuit can oscillate, the V_D range changes trend whereas the inductance increase gradually.

DownLoad: Full-Size Img PowerPoint

图 6 不同直流激励选择下, 逐步增大电感时振荡频率变化曲线　(a) V_D = 2.5 V; (b) V_D = 2.8 V; (c) V_D = 3.0 V; (d) V_D = 3.5 V

Figure 6. The oscillation frequency change curves when the inductance is gradually increased under different DC excitations: (a) V_D = 2.5 V; (b) V_D = 2.8 V; (c) V_D = 3.0 V; (d) V_D = 3.5 V.

DownLoad: Full-Size Img PowerPoint

图 7 N型LAM神经元电路的“全或无”行为

Figure 7. The “all-or-nothing” behavior of N-type LAM neuron circuit.

DownLoad: Full-Size Img PowerPoint

图 8 不同占空比的脉冲激励下, 神经元电路的发放行为波形　(a)占空比 = 0.01; (b)占空比 = 0.1; (c)占空比 = 0.4; (d)占空比 = 0.6; (e)占空比 = 0.8; (f)占空比 = 1.0

Figure 8. The firing behavior waveforms of the neuron circuit under pulse excitation with different duty ratios: (a) Duty ratio = 0.01; (b) duty ratio = 0. 1; (c) duty ratio = 0.4; (d) duty ratio = 0.6; (e) duty ratio = 0.8; (f) duty ratio = 1.0.

DownLoad: Full-Size Img PowerPoint

图 9 (a)生物感受系统结构示意图; (b)基于N型LAM的人工触觉神经元结构图

Figure 9. (a) Schematic diagram of the biological sensor system; (b) the structure diagram of the artificial tactile neuron based on the N-type LAM.

DownLoad: Full-Size Img PowerPoint

图 10 L = 300 mH时, 不同直流激励下人工神经元电路中N型LAM两端电压v的瞬时时域波形

Figure 10. The instantaneous time-domain waveforms of the voltage across the N-type LAM in the artificial neuron circuit under different DC excitations with L = 300 mH.

DownLoad: Full-Size Img PowerPoint

图 11 不同电感下, 递增直流电压下振荡频率变化曲线　(a) L = 300 mH; (b) L = 500 mH

Figure 11. Oscillation frequency varies as a function of DC voltage under different inductances: (a) L = 300 mH; (b) L = 500 mH.

DownLoad: Full-Size Img PowerPoint

图 12 (a) 基于N型LAM的硬件仿真器原理图; (b) 实验设备图

Figure 12. (a) Schematic diagram of hardware emulatorof the N-type LAM; (b) diagram of experimental equipments.

DownLoad: Full-Size Img PowerPoint

图 13 (a) 实验测量N型LAM硬件仿真器的DC V-I特性曲线; (b) 实验测量N型LAM硬件仿真器电导变化曲线

Figure 13. (a) Experimental measurement of the DC V-I characteristics curve of the N-type LAM hardware emulator; (b) experimental measurement of the conductance change curve of the N-type LAM hardware emulator.

DownLoad: Full-Size Img PowerPoint

图 14 人工神经元仿真器电路结构图

Figure 14. Circuit structure diagram of artificial neuron emulator.

DownLoad: Full-Size Img PowerPoint

图 15 实验测量得到人工神经元的“全或无”行为

Figure 15. Experimentally measured the “all-or-nothing” behavior of artificial neuron emulator.

DownLoad: Full-Size Img PowerPoint

图 16 增大脉冲宽度, 实验测得神经元的发放行为波形　(a)占空比为0.15; (b)占空比为0.40; (c)占空比为0.65; (d)占空比为0.85

Figure 16. Increasing the pulse width, the experimentally measured neuron firing behavior waveforms: (a) Duty ratio is 0.15; (b) duty ratio is 0.40; (c) duty ratio is 0.65; (d) duty ratio is 0.85.

DownLoad: Full-Size Img PowerPoint

图 17 直流偏置V_D = 3 V时, 不同电感选择下实验测得人工神经元电路输出v的瞬时时域波形　(a) L = 30 mH; (b) L = 39 mH; (c) L = 47 mH; (d) L = 100 mH; (e) L = 200 mH; (f) L = 300 mH

Figure 17. The experimentally measured instantaneous time-domain waveforms of the artificial neuron circuit output v under different inductances with the DC bias V_D = 3 V: (a) L = 30 mH; (b) L = 39 mH; (c) L = 47 mH ; (d) L = 100 mH; (e) L = 200 mH; (f) L = 300 mH

DownLoad: Full-Size Img PowerPoint

图 18 电感L = 300 mH时, 不同直流偏置选择下实验测得N型LAM两端电压v的瞬时时域波形　(a) V_D = 2.5 V; (b) V_D = 2.8 V; (c) V_D = 3.5 V; (d) V_D = 4.0 V; (e) V_D = 4.4 V; (f) V_D = 4.8 V

Figure 18. The instantaneous time-domain waveforms of the voltage v across the N-type LAM measured under different DC bias selections with the inductance L = 300 mH: (a) V_D = 2.5 V; (b) V_D = 2.8 V; (c) V_D = 3.5 V; (d) V_D = 4.0 V; (e) V_D = 4.4 V; (f) V_D = 4.8 V

DownLoad: Full-Size Img PowerPoint

图 19 两种电感选择下, 递增直流激励实验测得v的频率变化曲线　(a) L = 330 mH; (b) L = 470 mH

Figure 19. The experimentally measured frequency characteristics increasing the DC excitation gradually under two different inductances: (a) L = 330 mH; (b) L = 470 mH.

DownLoad: Full-Size Img PowerPoint

表 1 硬件电路参数数值

Table 1. Hardware circuit parameter value.

参数取值参数取值参数取值参数取值

V_CC,V_s/V +15 R_i2/kΩ 40 R_d1/kΩ 2.5 R_in/kΩ 1
V_EE/V –15 R_x/kΩ 10 R_d0/kΩ 62.5 C_i/nF 1
R_i1/kΩ 44.44 R_p/kΩ 50 R_w,R_z/kΩ 5

DownLoad: CSV

map

[1]	Moore G E 1998 Proc. IEEE 86 82 Google Scholar
[2]	Backus J 1978 Commun. ACM. 21 613 Google Scholar
[3]	Zhao Y, Liu B, Yang J, He J, Jiang J 2020 Chin. Phys. Lett. 37 088501 Google Scholar
[4]	Chen Y-B, Yang X-K, Yan T, Wei B, Cui H-Q, Li C, Cai L 2020 Chin. Phys. Lett. 37 078501 Google Scholar
[5]	Kumar S, Williams R S, Wang Z 2020 Nature 585 518
[6]	Maass W 1997 Neural. Netw. 10 659 Google Scholar
[7]	Merolla P A, Arthur J V, Alvarez-Icaza R, et al. 2014 Science 345 668 Google Scholar
[8]	Davies M, Srinivasa N, Lin T H, et al. 2018 IEEE Micro. 38 82 Google Scholar
[9]	Indiveri G, Linares-Barranco B, Hamilton T J, et al. 2011 Front. Neurosci. 5 73 Google Scholar
[10]	Kim H, Hwang S, Park J, Yun S, Lee J H, Park B G 2018 IEEE Electron. Device Lett. 39 630 Google Scholar
[11]	Wang W, Pedretti G, Milo V, Carboni R, Calderoni A, Ramaswamy N, Spinelli A S, Ielmini D 2018 Sci. Adv. 4 eaat4752 Google Scholar
[12]	Prezioso M, Mahmoodi M R, Bayat F M, Nili H, Kim H, Vincent A, Strukov D B 2018 Nat. Commun. 9 5311 Google Scholar
[13]	Wang Z, Joshi S, Savel’ev S, et al. 2018 Nat. Electron. 1 137 Google Scholar
[14]	Roy K, Jaiswal A, Panda P 2019 Nature 575 607 Google Scholar
[15]	Wang M, Cai S, Pan C, Wang C, Lian X, Zhuo Y, Xu K, Cao T, Pan X, Wang B, Liang S J, Yang J J, Wang P, Miao F 2018 Nat. Electron. 1 130 Google Scholar
[16]	Pickett M D, Williams R S 2012 Nanotechnology 23 215202 Google Scholar
[17]	Choi S, Tan S H., Li Z, Kim Y, Choi C, Chen P Y, Yeon H, Yu S, Kim J 2018 Nat. Mater. 17 335 Google Scholar
[18]	Li C, Hu M, Li Y, et al. 2018 Nat. Electron. 1 52 Google Scholar
[19]	Hu M, Graves C E, Li C, Li Y, Ge N, Montgomery E, Davila N, Jiang H, Williams R S, Yang J J, Xia Q, Strachan J P 2018 Adv. Mater. 30 1705914 Google Scholar
[20]	Valov I, Linn E, Tappertzhofen S, Schmelzer S, van den Hurk J, Lentz F, Waser R 2013 Nat. Commun. 4 1771 Google Scholar
[21]	Wang Z, Rao M, Han J W, et al. 2018 Nat. Commun. 9 3208 Google Scholar
[22]	Yang Y, Gao P, Li L, Pan X, Tappertzhofen S, Choi S, Waser R, valov I, Lu W D. 2014 Nat. Commun. 5 4232 Google Scholar
[23]	Liang Y, Wang G, Chen G, Dong Y, Yu D, Iu H H C 2020 IEEE Trans. Circuits. Syst. I. Regul. Pap. 67 5139 Google Scholar
[24]	Li C, Wang Z, Rao M, Belkin D, Song W, Jiang H, Yan P, Li Y, Lin P, Hu M, Ge N, Stranchan J P, Barnell M, Wu Q, Williams R S, Yang J J, Xia Q 2019 Nat. Mach. Intell. 1 49 Google Scholar
[25]	Li C, Belkin D, Li Y, Yan P, Hu M, Ge N, Jiang H, Montgomery E, Lin P, Wang Z, Song W, Strachan J P, Barnell M, Wu Q, Williams R S, Yang J J, Xia Q 2018 Nat. Commun. 9 2385 Google Scholar
[26]	Zhang C, Chen Y, Yi M, Zhu Y, Li T, Liu L, Wang L, Xie L, Huang W 2018 Sci. Sin. Inform. 48 115 Google Scholar
[27]	Chua L O 2005 Int. J. Bifurcat. Chaos. 15 3435 Google Scholar
[28]	Mainzer K, Chua L O 2013 Local Activity Principle (London: Imperial College Press)
[29]	Midya R, Wang Z, Asapu S, Joshi S, Li Y, Zhuo Y, Song W, Jiang H, Upadhay N, Rao M, Lin P, Li C, Xia Q, Yang J J 2019 Adv. Electron. Mater. 5 1900060 Google Scholar
[30]	Zhu J, Wu Z, Zhang X, Wang Y, Lu J, Chen P, Cheng L, Shi T, Liu Q 2021 5th IEEE Electron Devices Technology & Manufacturing Conference Chengdu, China, March 9–12, 2021 pp1–3
[31]	Al-Shedivat M, Naous R, Cauwenberghs G, Salama K N 2015 IEEE J. Emerg. Sel. Topic. Power Electon. 5 242 Google Scholar
[32]	Zhang X, Zhuo Y, Luo Q, Wu Z, Midya R, Wang Z, Song W, Wang R, Upadhyay N K, Fang Y, Kiani F, Rao M, Yang Y, Xia Q, Liu Q, Liu M, Yang J J 2020 Nat. Commun. 11 51 Google Scholar
[33]	Chua L O 2011 Appl. Phys. A 102 765 Google Scholar
[34]	Liang Y, Lu Z, Wang G, Dong Y, Yu D, Iu H H C 2020 IEEE Access 8 75571 Google Scholar

[1]	Guo Hui-Meng, Liang Yan, Dong Yu-Jiao, Wang Guang-Yi. Simplification of Chua corsage memristor and hardware implementation of its neuron circuit. Acta Physica Sinica, 2023, 72(7): 070501. doi: 10.7498/aps.72.20222013
[2]	Gu Ya-Na, Liang Yan, Wang Guang-Yi, Xia Chen-Yang. Design of NbO_x memristive neuron and its application in spiking neural networks. Acta Physica Sinica, 2022, 71(11): 110501. doi: 10.7498/aps.71.20220141
[3]	Liu Yi-Chun, Lin Ya, Wang Zhong-Qiang, Xu Hai-Yang. Oxide-based memristive neuromorphic synaptic devices. Acta Physica Sinica, 2019, 68(16): 168504. doi: 10.7498/aps.68.20191262
[4]	Shao Nan, Zhang Sheng-Bing, Shao Shu-Yuan. Mathematical model of memristor with sensory memory. Acta Physica Sinica, 2019, 68(1): 018501. doi: 10.7498/aps.68.20181577
[5]	Shao Nan, Zhang Sheng-Bing, Shao Shu-Yuan. Analysis of memristor model with learning-experience behavior. Acta Physica Sinica, 2019, 68(19): 198502. doi: 10.7498/aps.68.20190808
[6]	Xu Wei, Wang Yu-Qi, Li Yue-Feng, Gao Fei, Zhang Miao-Cheng, Lian Xiao-Juan, Wan Xiang, Xiao Jian, Tong Yi. Design of novel memristor-based neuromorphic circuit and its application in classical conditioning. Acta Physica Sinica, 2019, 68(23): 238501. doi: 10.7498/aps.68.20191023
[7]	Chen Yi-Hao, Xu Wei, Wang Yu-Qi, Wan Xiang, Li Yue-Feng, Liang Ding-Kang, Lu Li-Qun, Liu Xin-Wei, Lian Xiao-Juan, Hu Er-Tao, Guo Yu-Feng, Xu Jian-Guang, Tong Yi, Xiao Jian. Fabrication of synaptic memristor based on two-dimensional material MXene and realization of both long-term and short-term plasticity. Acta Physica Sinica, 2019, 68(9): 098501. doi: 10.7498/aps.68.20182306
[8]	Wu Quan-Tan, Shi Tuo, Zhao Xiao-Long, Zhang Xu-Meng, Wu Fa-Cai, Cao Rong-Rong, Long Shi-Bing, Lü Hang-Bing, Liu Qi, Liu Ming. Two-dimensional hexagonal boron nitride based memristor. Acta Physica Sinica, 2017, 66(21): 217304. doi: 10.7498/aps.66.217304
[9]	Shao Nan, Zhang Sheng-Bing, Shao Shu-Yuan. Modification of memristor model with synaptic characteristics and mechanism analysis of the model's learning-experience behavior. Acta Physica Sinica, 2016, 65(12): 128503. doi: 10.7498/aps.65.128503
[10]	Xu Ya-Ming, Wang Li-Dan, Duan Shu-Kai. A memristor-based chaotic system and its field programmable gate array implementation. Acta Physica Sinica, 2016, 65(12): 120503. doi: 10.7498/aps.65.120503
[11]	Ruan Jing-Ya, Sun Ke-Hui, Mou Jun. Memristor-based Lorenz hyper-chaotic system and its circuit implementation. Acta Physica Sinica, 2016, 65(19): 190502. doi: 10.7498/aps.65.190502
[12]	Lu Jin-Bo, Hou Xiao-Rong, Luo Min. General robust stability controller design method for a class of hopf bifurcation systems. Acta Physica Sinica, 2016, 65(6): 060502. doi: 10.7498/aps.65.060502
[13]	Liu Yu-Dong, Wang Lian-Ming. Application of memristor-based spiking neural network in image edge extraction. Acta Physica Sinica, 2014, 63(8): 080503. doi: 10.7498/aps.63.080503
[14]	Zhang Ling-Mei, Zhang Jian-Wen, Wu Run-Heng. Anti-control of Hopf bifurcation in the new chaotic system with piecewise system and exponential system. Acta Physica Sinica, 2014, 63(16): 160505. doi: 10.7498/aps.63.160505
[15]	Li Zhi-Jun, Zeng Yi-Cheng, Li Zhi-Bin. Memristive chaotic circuit based on modified SC-CNNs. Acta Physica Sinica, 2014, 63(1): 010502. doi: 10.7498/aps.63.010502
[16]	Zhao Hong-Yong, Chen Ling, Yu Xiao-Hong. Bifurcation and control of a class of inertial neuron networks. Acta Physica Sinica, 2011, 60(7): 070202. doi: 10.7498/aps.60.070202
[17]	Bao Bo-Cheng, Hu Wen, Xu Jian-Ping, Liu Zhong, Zou Ling. Analysis and implementation of memristor chaotic circuit. Acta Physica Sinica, 2011, 60(12): 120502. doi: 10.7498/aps.60.120502
[18]	Wu Zhi-Qiang, Sun Li-Ming. Hopf bifurcation control of the Rössler system based on Washout filter controller. Acta Physica Sinica, 2011, 60(5): 050504. doi: 10.7498/aps.60.050504
[19]	Ma Wei, Wang Ming-Yu, Nie Hai-Long. Control of Hopf bifurcation in the one-cycle controlled Boost converter and its experimental implementation. Acta Physica Sinica, 2011, 60(10): 100202. doi: 10.7498/aps.60.100202
[20]	Zhang Chao-Xia, Yu Si-Min. Wireless chaotic speech communication via digital signal processor ——system design and hardware implementation. Acta Physica Sinica, 2010, 59(5): 3017-3026. doi: 10.7498/aps.59.3017

Catalog

Vol. 71, Issue 5 - 2022-03-05

Metrics

Abstract views: 6103
PDF Downloads: 193
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板