SCIENTIA SINICA Informationis, Volume 48 , Issue 2 : 115-142(2018) https://doi.org/10.1360/N112017-00022

Recent progress in memristors for stimulating synaptic plasticity

Chenxi ZHANG 1,2,3, Yan CHEN 1,2,3, Mingdong YI 1,2,3,*, Ying ZHU 1,2,3, Tengfei LI 1,2,3, Lutao LIU 1,2,3, Laiyuan WANG 1,2,3,*, Linghai XIE 1,2,3, Wei HUANG 1,2,3,4,5,*
More info
  • ReceivedJan 23, 2017
  • AcceptedJul 21, 2017
  • PublishedJan 8, 2018


Funded by






长江学者和创新团队(IRT_ 15R37)




[1] Jo S H, Chang T, Ebong I, et al. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett, 2010, 10: 1297--1301. Google Scholar

[2] Smith L S. Implementing neural models in silicon. In: Handbook of Nature-Inspired and Innovative Computing. Berlin: Springer, 2006, 433--475. Google Scholar

[3] Izhikevich E M, Edelman G M. Large-scale model of mammalian thalamocortical systems. Proc Natl Acad Sci, 2008, 105: 3593--3598. Google Scholar

[4] Indiveri G, Chicca E, Douglas R. A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity. IEEE Trans Neural Netw, 2006, 17: 211--221. Google Scholar

[5] Chua L. Memristor-the missing circuit element. IEEE Trans Circuit Theory, 1971, 18: 507--519. Google Scholar

[6] Qi J, Li C, Huang T. Stability of delayed memristive neural networks with time-varying impulses. Cogn Neurodyn, 2014, 8: 429--436. Google Scholar

[7] Tang Y, Nyengaard J R, de Groot D M, et al. Total regional and global number of synapses in the human brain neocortex. Synapse, 2001, 41: 258--273. Google Scholar

[8] Alibart F, Pleutin S, Guerin D, et al. An organic nanoparticle transistor behaving as a biological spiking synapse. Adv Funct Mater, 2010, 20: 330--337. Google Scholar

[9] Lai Q X, Zhang L, Li Z Y, et al. Ionic/Electronic hybrid materials integrated in a synaptic transistor with signal processing and learning functions. Adv Mater, 2010, 22: 2448--2453. Google Scholar

[10] Ohno T, Hasegawa T, Tsuruoka T, et al. Short-term plasticity and long-term potentiation mimicked in single inorganic synapses. Nat Mater, 2011, 10: 591--595. Google Scholar

[11] Josberger E E, Deng Y X, Sun W, et al. Two-terminal protonic devices with synaptic-like short-term depression and device memory. Adv Mater, 2014, 26: 4986--4990. Google Scholar

[12] Rachmuth G, Poon C S. Transistor analogs of emergent iono-neuronal dynamics. Hfsp Journal, 2008, 2: 156--166. Google Scholar

[13] Liu Y H, Zhu L Q, Feng P, et al. Freestanding artificial synapses based on laterally proton-coupled transistors on chitosan membranes. Adv Mater, 2015, 27: 5599--5604. Google Scholar

[14] Lont J B, Guggenbuhl W. Analog CMOS implementation of a multilayer perceptron with nonlinear synapses. IEEE Trans Neural Netw, 1992, 3: 457--465. Google Scholar

[15] He W, Huang K J, Ning N, et al. Enabling an integrated rate-temporal learning scheme on memristor. Sci Rep, 2014, 4: 4755. Google Scholar

[16] Li Y, Zhong Y P, Zhang J J, et al. Activity-dependent synaptic plasticity of a chalcogenide electronic synapse for neuromorphic systems. Sci Rep, 2014, 4: 4906. Google Scholar

[17] Linares-Barranco B, Serrano-Gotarredona T. Memristance can explain spike-time-dependent-plasticity in neural synapses. Nat Precedings, 2009, 1. Google Scholar

[18] Perea G, Navarrete M, Araque A. Tripartite synapses: astrocytes process and control synaptic information. Trends Neurosci, 2009, 32: 421--431. Google Scholar

[19] Kornijcuk V, Kavehei O, Lim H, et al. Multiprotocol-induced plasticity in artificial synapses. Nanoscale, 2014, 6: 15151--15160. Google Scholar

[20] Chang T, Jo S H, Lu W. Short-term memory to long-term memory transition in a nanoscale memristor. ACS Nano, 2011, 5: 7669--7676. Google Scholar

[21] Abbott L F, Nelson S B. Synaptic plasticity: taming the beast. Nat Neurosci, 2000, 3: 1178--1183. Google Scholar

[22] Bi G Q, Poo M M. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. Neurosci, 1998, 18: 10464--10472. Google Scholar

[23] Hebb D O. The organization of behavior: a neuropsychological approach. American J Psychol, 1949, 63: 633. Google Scholar

[24] Wixted J T, Ebbesen E B. On the form of forgetting. Psychol Sci, 1991, 2: 409--415. Google Scholar

[25] Douglas R, Mahowald M, Mead C. Neuromorphic analogue VLSI. Annu Rev Neurosci, 1995, 18: 255--281. Google Scholar

[26] Li H T. Study on material selection and behavior mechanism of membrane membrane. Dissertation for Masters Degree. Nanjing: Nanjing University, 2011. Google Scholar

[27] Strukov D B, Snider G S, Stewart D R, et al. The missing memristor found. Nature, 2008, 453: 80--83. Google Scholar

[28] Cantley K D, Subramaniam A, Stiegler H J, et al. Hebbian learning in spiking neural networks with nanocrystalline silicon TFTs and memristive synapses. IEEE Trans Nanotechnol, 2011, 10: 1066--1073. Google Scholar

[29] Kim K H, Gaba S, Wheeler D, et al. A functional hybrid memristor crossbar-array/CMOS system for data storage and neuromorphic applications. Nano Lett, 2012, 12: 389--395. Google Scholar

[30] Chen L, Li C D, Wang X, et al. Associate learning and correcting in a memristive neural network. Neural Comput Appl, 2013, 22: 1071--1076. Google Scholar

[31] Guo X, Tan Z H, Yin X B, et al. Memristive ionic devices for information storage, logic operations and brain neural function. Chin Sci Bull, 2014, 59: 2926--2936. Google Scholar

[32] Zhang C, Tai Y T, Shang J, et al. Synaptic plasticity and learning behaviours in flexible artificial synapse based on polymer/viologen system. J Mater Chem, 2016, 4: 3217--3223. Google Scholar

[33] Citri A, Malenka R C. Synaptic plasticity: multiple forms, functions, and mechanisms. Neuropsychopharmacol, 2008, 33: 18--41. Google Scholar

[34] Zucker R S. Short-term synaptic plasticity. Annu Rev Neurosci, 1989, 12: 13--31. Google Scholar

[35] Zucker R S. Calcium and activity-dependent synaptic plasticity. Curr Opin Neurobiol, 1999, 9: 305--313. Google Scholar

[36] Bliss T V, L Mo T. Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. J Psychol, 1973, 232: 331--356. Google Scholar

[37] Larkman A U, Jack J J B. Synaptic plasticity: hippocampal LTP. Curr Opin Neurobiol, 1995, 5: 324--334. Google Scholar

[38] Katz B, Miledi R. The role of calcium in neuromuscular facilitation. J Psychol, 1968, 195: 481--492. Google Scholar

[39] Kandel E R. The molecular biology of memory storage: a dialogue between genes and synapses. Science, 2001, 294: 1030--1038. Google Scholar

[40] Dobrunz L E, Stevens C F. Heterogeneity of release probability, facilitation, and depletion at central synapses. Neuron, 1997, 18: 995--1008. Google Scholar

[41] Bao J X, Kandel E R, Hawkins R D. Involvement of pre- and postsynaptic mechanisms in posttetanic potentiation at Aplysia synapses. Science, 1997, 275: 969--973. Google Scholar

[42] Martin S, Grimwood P, Morris R. Synaptic plasticity and memory: an evaluation of the hypothesis. Annu Rev Neurosci, 2000, 23: 649--711. Google Scholar

[43] Whitlock J R, Heynen A J, Shuler M G, et al. Learning induces long-term potentiation in the hippocampus. Science, 2006, 313: 1093--1097. Google Scholar

[44] Seo K, Kim I, Jung S, et al. Analog memory and spike-timing-dependent plasticity characteristics of a nanoscale titanium oxide bilayer resistive switching device. Nanotechnology, 2011, 22: 223--254. Google Scholar

[45] Zhang J, Sun H, Li Y, et al. AgInSbTe memristor with gradual resistance tuning. Appl Phys Lett, 2013, 102: 183513. Google Scholar

[46] Li S, Zeng F, Chen C, et al. Synaptic plasticity and learning behaviours mimicked through Ag interface movement in an Ag/conducting polymer/Ta memristive system. J Mater Chem, 2013, 1: 5292--5298. Google Scholar

[47] Wang Z Q, Xu H Y, Li X H, et al. Synaptic learning and memory functions achieved using oxygen ion migration/diffusion in an amorphous InGaZnO memristor. Adv Funct Mater, 2012, 22: 2759--2765. Google Scholar

[48] Hu S, Liu Y, Chen T, et al. Emulating the paired-pulse facilitation of a biological synapse with a NiOx-based memristor. Appl Phys Lett, 2013, 102: 183510. Google Scholar

[49] Wang Z, Joshi S, Savelev S E, et al. Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing. Nat Mater, 2017, 16: 101--108. Google Scholar

[50] Yang J J, Pickett M D, Li X M, et al. Memristive switching mechanism for metal/oxide/metal nanodevices. Nat Nanotechnol, 2008, 3: 429--433. Google Scholar

[51] Chang T, Jo S H, Kim K H, et al. Synaptic behaviors and modeling of a metal oxide memristive device. Appl Phys A: Mater Sci Process, 2011, 102: 857--863. Google Scholar

[52] Lamprecht R, LeDoux J. Structural plasticity and memory. Nat Rev Neurosci, 2004, 5: 45--54. Google Scholar

[53] Nayak A, Ohno T, Tsuruoka T, et al. Controlling the synaptic plasticity of a Cu2S gap-type atomic switch. Adv Funct Mater, 2012, 22: 3606--3613. Google Scholar

[54] Liu G, Wang C, Zhang W, et al. Organic biomimicking memristor for information storage and processing applications. Adv Electron Mater, 2016, 2: 1500298. Google Scholar

[55] Shirota Y. Photo and electroactive amorphous molecular materials molecular design, syntheses, reactions, properties, and applications. J Mater Chem, 2005, 15: 75--93. Google Scholar

[56] Song Y, Di C A, Yang X, et al. A cyclic triphenylamine dimer for organic field-effect transistors with high performance. J Am Chem Soc, 2006, 128: 15940--15941. Google Scholar

[57] Kumar R, Pillai R G, Pekas N, et al. Spatially resolved raman spectroelectrochemistry of solid-state polythiophene/viologen memory devices. J Am Chem Soc, 2012, 134: 14869--14876. Google Scholar

[58] Mortimer R J, Dyer A L, Reynolds J R. Electrochromic organic and polymeric materials for display applications. Displays, 2006, 27: 2--18. Google Scholar

[59] Han B, Li Z, Wandlowski T, et al. Potential-induced redox switching in viologen self-assembled monolayers: an ATR-SEIRAS approach. J Phy Chem C, 2007, 111: 18355--13863. Google Scholar

[60] ChenY, Liu G, Wang C, et al. Polymer memristor for information storage and neuromorphic application. Mater Horiz, 2014, 1: 489--506. Google Scholar

[61] Erokhin V, Berzina T, Gorshkov K, et al. Stochastic hybrid 3D matrix: learning and adaptation of electrical properties. J Mater Chem, 2012, 22: 22881--22887. Google Scholar

[62] Wang C, Liu G, Chen Y, et al. Synthesis and nonvolatile memristive switching effect of a donor-acceptor structured oligomer. J Mater Chem C, 2015, 3: 664--673. Google Scholar

[63] Wen G, Ren Z, Sun D, et al. Synthesis of alternating copolysiloxane with terthiophene and perylenediimide derivative pendants for involatile WORM memory device. Adv Funct Mater, 2014, 24: 3446--3455. Google Scholar

[64] Sun D, Yang Z, Ren Z, et al. Oligosiloxane functionalized with pendant (1,3-Bis(9-carbazolyl)benzene) (mCP) for solution-processed organic electronics. Chem Eur J, 2014, 20: 16233--16241. Google Scholar

[65] Rao R P, Sejnowski T J. Spike-timing-dependent Hebbian plasticity as temporal difference learning. Neural Comput, 2001, 13: 2221--2237. Google Scholar

[66] Gerstner W, Ritz R, Hemmen J L V. Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns. Biol Cybern, 1993, 69: 503--515. Google Scholar

[67] Saudargiene A, Porr B, Worgotter F. How the shape of pre-and postsynaptic signals can influence STDP: a biophysical model. Neural Comput, 2004, 16: 595--625. Google Scholar

[68] Masquelier T, Guyonneau R, Thorpe S J. Spike timing dependent plasticity finds the start of repeating patterns in continuous spike trains. Plos One, 2008, 3: 1377. Google Scholar

[69] Masquelier T, Guyonneau R, Thorpe S J. Competitive STDP-based spike pattern learning. Neural Comput, 2009, 21: 1259--1276. Google Scholar

[70] Young J M, Waleszczyk W J, Wang C, et al. Cortical reorganization consistent with spike timing-but not correlation-dependent plasticity. Nat Neurosci, 2007, 10: 887--895. Google Scholar

[71] Finelli L A, Haney S, Bazhenov M, et al. Synaptic learning rules and sparse coding in a model sensory system. Plos Comput Biol, 2008, 4: 1000062. Google Scholar

[72] Bi G Q, Poo M M. Synaptic modification by correlated activity: Hebbs postulate revisited. Annu Rev Neurosci, 2001, 24: 139--166. Google Scholar

[73] Li Y, Zhong Y, Xu L, et al. Ultrafast synaptic events in a chalcogenide memristor. Sci Rep, 2013, 3: 1619. Google Scholar

[74] Pershin Y V, Diventra M. Experimental demonstration of associative memory with memristive neural networks. Neural Netw, 2010, 23: 881--886. Google Scholar

[75] Pickett M D, Medeiros-Ribeiro G, Williams R S. A scalable neuristor built with Mott memristors. Nat Mater, 2013, 12: 114--117. Google Scholar

[76] Yang J, Wang L D, Duan S K. An anti-series memristive synapse circuit design and its application. Sci Sin Inform, 2016, 46: 391--403. Google Scholar

[77] Anderson J R. Language, Memory and Thought. Hillsdale: LEA, 1976. Google Scholar

[78] Pavlov I P, Anrep G V. Conditioned Reflexes. Mineola: Dover Publications, 2003. Google Scholar

[79] Turrigiano G G, Nelson S B. Homeostatic plasticity in the developing nervous system. Nat Rev Neurosci, 2004, 5: 97--107. Google Scholar

[80] Malenka R C, Bear M F. LTP and LTD: an embarrassment of riches. Neuron, 2004, 44: 21--25. Google Scholar

[81] Miller K D. Synaptic economics: competition and cooperation in synaptic plasticity. Neuron, 1996, 17: 371--374. Google Scholar

[82] Miller K D, Mackay D J C. The role of constraints in hebbian learning. Neural Comput, 1994, 6: 100--126. Google Scholar

[83] Sullivan T J, de Sa V R. Homeostatic synaptic scaling in self-organizing maps. Neural Netw, 2006, 19: 734--743. Google Scholar

[84] Turrigiano G G, Leslie K R, Desai N S, et al. Activity-dependent scaling of quantal amplitude in neocortical neurons. Nature, 1998, 391: 892--896. Google Scholar

[85] Davis G W. Homeostatic control of neural activity: from phenomenology to molecular design. Annu Rev Neurosci, 2006, 29: 307--323. Google Scholar

[86] Turrigiano G G. The self-tuning neuron: synaptic scaling of excitatory synapses. Cell, 2008, 135: 422--435. Google Scholar

[87] Yang X, Fang Y, Yu Z, et al. Nonassociative learning implementation by a single memristor-based multi-terminal synaptic device. Nanoscale, 2016, 8: 18897--18904. Google Scholar

[88] Yu S, Gao B, Fang Z, et al. A low energy oxide-based electronic synaptic device for neuromorphic visual systems with tolerance to device variation. Adv Mater, 2013, 25: 1774--1779. Google Scholar

[89] Xiong F, Liao A D, Esterada D, et al. Low-power switching of phase-change materials with carbon nanotube electrodes. Science, 2011, 332: 568--570. Google Scholar

[90] Pecevski D, Buesing L, Maass W. Probabilistic inference in general graphical models through sampling in stochastic networks of spiking neurons. Plos Comput Biol, 2011, 7: 1002294. Google Scholar

[91] Tuma T, PantaziA, Le G M, et al. Stochastic phase-change neurons. Nat Nanotechnol, 2016, 11: 693--699. Google Scholar

[92] Jo S H, Kim K H, Lu W. High-density crossbar arrays based on a Si memristive system. Nano Lett, 2009, 9: 870--874. Google Scholar

[93] Kim K H, Kang B S, Lee M J, et al. Multilevel programmable oxide diode for cross-point memory by electrical-pulse-induced resistance change. IEEE Electron Device Lett, 2009, 30: 1036--1038. Google Scholar

[94] Xia Q, Robinett W, Cumbie M W, et al. Memristor-CMOS hybrid integrated circuits for reconfigurable logic. Nano Lett, 2009, 9: 3640--3645. Google Scholar

[95] Robinett W, Pickett M, Borghetti J, et al. A memristor-based nonvolatile latch circuit. Nanotechnol, 2010, 21: 235203. Google Scholar

[96] Pershin Y V, Ventra M D. Practical approach to programmable analog circuits with memristors. IEEE Trans Circ Syst I: Regul Papers, 2010, 57: 1857--1864. Google Scholar

[97] Berzina T, Smerieri A, Bernabò M, et al. Optimization of an organic memristor as an adaptive memory element. J Appl Phys, 2009, 105: 124515. Google Scholar

[98] Choi H, Jung H, Lee J, et al. An electrically modifiable synapse array of resistive switching memory. Nanotechnol, 2009, 20: 345201. Google Scholar

[99] Liu D Q, Cheng H F, Zhu X, et al. Progress in memristor and its resistance mechanism. Acta Phys Sin, 2014, 18: 8--20. Google Scholar

[100] Pan F, Gao S, Chen C, et al. Recent progress in resistive random access memories: materials, switching mechanisms, and performance. Mater Sci Eng R Rep, 2014, 83: 51--59. Google Scholar

[101] Hu S, Wu S, Jia W, et al. Review of nanostructured resistive switching memristor and its applications. Nano Sci Nano Technol Lett, 2014, 6: 729--757. Google Scholar

[102] Abraham W C, Bear M F. Metaplasticity: the plasticity of synaptic plasticity. Trends Neurosci, 1996, 19: 126--130. Google Scholar

[103] Bear M F, Cooper L N, Ebner F F. A physiological-basis for a theory of synapse modification. Science, 1987, 237: 42--48. Google Scholar

  • Figure 1

    (Color online) The connections between neurons. (a) A synapse is where a pre-synaptic neuron “connects with a post-synaptic neuron; (b) detail of synaptic junction [17]@Copyright 2009 Nature Publishing Group

  • Figure 2

    (Color online) Examples of experiments illustrating (a) LTP and (b) LTD. Synaptic weight, defined as the initial slope of the field excitatory postsynaptic potential (fEPSP slope) is plotted as a function of time [33]@Copyright 2008 Nature Publishing Group

  • Figure 3

    (Color online) (a) Ag/Si Memristor response to programming pulses (LTP/LTD). The device conductance can be incrementally increased or decreased by consecutive potentiating or depressing pulses. The conductance was measured at 1 V after each pulse and the read current is plotted. P, 3.2 V, 300 $\mu$s; D, $-$2.8 V, 300 $\mu$s @Copyright 2010 American Chemical Society; (b) magnitude of the paired-pulse facilitation (PPF) of a NiO$_{x}$-based memristor as a function of the pulse interval [1]@Copyright 2013 AIP Publishing LLC

  • Figure 4

    (Color online) (a) DC I-V curves of Pd/WO$_{x}$/W memristor studied here. Positive voltage sweeps (numberedprotectłinebreak 1 $\sim$ 5, +1.2 V, 2 V/s) and negative voltage sweeps (6 $\sim$ 10, $-$1.2 V, 2 V/s) increase and decrease the memristor conductance continuously, respectively; (b) schematic illustration of oxygen vacancy diffusion in the memristor device [20]@Copyright 2011 American Chemical Society

  • Figure 5

    (Color online) (a) A retention curve of the memristor; (b) a forgetting curve of human memory; (c) the voltage profile applied to the memristor, consisting of five +1.3 V, 1 ms pulses and a constant +0.3 V read voltage; (d) the corresponding current through the memristor data recorded continuously throughout the test [20]@Copyright 2011 American Chemical Society

  • Figure 6

    (Color online) (a),(b) Memory retention data recorded after different numbers of identical stimuli (dots) and fitted curves using the SEF (solid lines); (c) characteristic relaxation time ($\tau$) obtained and the current $I_{0}$ plotted with respect to the number of stimulations ($N$); (d) the distribution and diffusion of oxygen vacancy after the application of a number of stimulates [20]@Copyright 2011 American Chemical Society

  • Figure 7

    (Color online) (a) Current through the memristor recorded after each stimulation pulse, at different pulse interval conditions; (b) the current increase $\Delta~I~=~\Delta~I_{k}-~\Delta~I_{i}$ after every stimulus plotted against pulse number for different pulse interval conditions [20]@Copyright 2011 American Chemical Society

  • Figure 8

    (Color online) Implementation of the transition from short-term plasticity to long-term plasticity (and transition from short-term memory to long-term memory) in a Ag$_{2}$S memristor. (a) Application of pulses causes the precipitation of Ag atoms from the Ag$_{2}$S electrode, resulting in the formation of an Ag atomic bridge between the Ag$_{2}$S electrode and a counter metal electrode. When the precipitated Ag atoms do not form a bridge, the memristor works as short-term plasticity (and short-term memory). After an atomic bridge is formed, it works as long-term plasticity (and long-term memory); (b) and (c) changes in the conductance of the inorganic synapse caused by the input pulses with different pulse intervals. Smaller interval can more effectively realize the transition from short-term plasticity to long-term plasticity [10]@Copyright 2011 Nature Publishing Group

  • Figure 9

    (Color online) Schematic illustration of a Cu$_{2}$S gap-type atomic switch in sensory memory (SM), short-term memory (STM), and long-term memory (LTM) states depending on the interval ($T$) of the input voltage pulse stimulation. The conductance ($G$) for a single atomic contact is given by $G_{0}=~77.5$ $\mu$S [53]@Copyright 2012 John Wiley and Sons

  • Figure 10

    (Color online) Changes in the conductance ($G$) of a Cu$_{2}$S inorganic synapse in vacuum at room temperature depending on the interval ($T$), amplitude ($V$), and width ($W$) of the input voltage pulse stimulation. (a) $V$=150 mV, $W$=500 mS, $T$=10 s; (b) $V$=150 mV, $W$=500 mS, $T$=1 s; (c) $V$=100 mV, $W$=500 mS, $T$=10 s; (d) $V$=150 mV, $W$=50 mS, $T$=1 s; (e) $V$=100 mV, $W$=500 mS, $T$=1 s; (f) the values of time constant ($\tau$) extracted from the fits of the conductance decay curves shown in the dashed rectangular box in (c). An exponential function, $y~=~y_{0}+~A{\rm~e}^{-t/~\tau}$, was used to fit the conductance curves [53]@Copyright 2012 John Wiley and Sons

  • Figure 11

    (Color online) Change in conductance ($G$) under ambient conditions for voltage pulse of amplitude ($V$) 150 mV and width ($W$) 500 mS at an interval ($T$) of 10 s [53]protectłinebreak @Copyright 2012 John Wiley and Sons

  • Figure 12

    (Color online) Temperature dependence of conductance ($G$) of a Cu$_{2}$S inorganic synapse in vacuum for input voltage pulses of amplitude = 150 mV, interval = 1 s, and width = 500 mS [53]@Copyright 2012 John Wiley and Sons

  • Figure 13

    (Color online) Implementation of SRDP in the AIST memristor, dependence of synaptic modification on the frequency of the postsynaptic firing rate. For postsynaptic firing rates below $f_{\theta}$ (50 kHz), the synapse is depressed, while synaptic potentiation can be observed beyond $f_{\theta}$. The presynaptic rate is fixed at 50 kHz [16]@Copyright 2014 Nature Publishing Group

  • Figure 14

    (Color online) SRDP of Ta/EV(CLO$_{4}$)$_{2}$/BTPA-F/Pt memristor. (a) Schematic illustration of the Ta/EV(CLO$_{4}$)$_{2}$/BTPA-F/Pt memristor and the biological synapse, (b) current and (c) current change ($\Delta~I$) with ten voltage pulse stimulations at different frequencies [54]@Copyright 2016 John Wiley and Sons

  • Figure 15

    (Color online) (a) Pre- and post-synaptic membrane voltages for the situation of positive $\Delta~T$, result in positive $v_{\rm~MR}$; (b) Pre- and post-synaptic membrane voltages for the situation of negative $\Delta~T$, result in negative $v_{\rm~MR}$ [17]@Copyright 2009 Nature Publishing Group

  • Figure 16

    (Color online) STDP experiental curve of Bi and Poo [72]@Copyright 2009 Nature Publishing Group

  • Figure 17

    (Color online) Demonstration of STDP in the memristor synapse. (a) The measured change of the memristor synaptic weight vs the relative timing $\Delta~t$ of the neuron spikes; (b) the measured change in excitatory postsynaptic current (EPSC) of hippocampal neurons vs the relative timing $\Delta~t$ of the neuron spikes [1]@Copyright 2010 American Chemical Society

  • Figure 18

    (Color online) Implementation of STDP with nanosecond-scale time windows in the chalcogenide synapse with the (a) antisymmetric Hebbian learning rule, (b) antisymmetric anti-Hebbian learning rule, (c) symmetric Hebbian learning rule, and (d) symmetric anti-Hebbian learning rule. The red dots indicate the experimental data and the blue lines are the fitted curves. The insets show the pre- and postsynaptic spike schemes and fitting functions [73]@Copyright 2013 Nature Publishing Group

  • Figure 19

    (Color online) Demonstration of the memory and forgetting function of human brain

  • Figure 20

    (Color online) Demonstration of the “learning – forgetting – relearning process of EV(ClO$_{4}$)$_{2}$/BTPA-F memristor. (a) The $1^{\rm~st}$ learning stage; (b) the $1^{\rm~st}$ forgetting stage; (c) the $2^{\rm~nd}$ learning stage; (d) the $2^{\rm~nd}$ forgetting stage; (e) the $3^{\rm~rd}$ learning stage [54]@Copyright 2016 John Wiley and Sons

  • Figure 21

    (Color online) The LTP/STP and “learning-experience behaviours and the dynamic model of device operation. (a) The nearly linear increase in the synaptic weight with consecutive stimuli; (b) the spontaneous decay of the conductivity, i.e., the relaxation process of STP, which is similar to the human-memory “forgetting curve; (c) re-stimulation process, which is similar to the “relearning process [47]@Copyright 2012 John Wiley and Sons

  • Figure 22

    (Color online) (a) The neural circuits of Pickett: two Mott memristors M$_{1}$ and M$_{2}$, with a characteristic parallel capacitance (C$_{1}$ and C$_{2}$, respectively), voltage sources and output device, (b) a — super-threshold input 0.3 V,protectłinebreak b — super-threshold output 0.33 V, c — sub-threshold input 0.2 V, d — sub-threshold output 28 mV [75]@Copyright 2013 Nature Publishing Group

  • Figure 23

    (Color online) (a),(b) The implementation of habituation. (a) Schematic of stimulus trains used for this measurement; (b) measured device current changes under the application of stimulus trains. (c),(d) The dependence of the habituation habituation behavioural response on stimulation rate. (c) The variation of recorded currents after every 10 stimulation pulses at four different pulse interval; (d) current increase ($\Delta~I$) plotted against pulse number under different pulse interval conditions [87]@Copyright 2016 Royal Society of Chemistry

  • Figure 24

    (Color online) The implementation of sensitization. (a) The modulatory effect of NMOS transistor, the current measured under every gate voltage was represented by different colours; (b)two forms of measured currents changed against the repetition of two different stimulation trains respectively [87]@Copyright 2016 Royal Society of Chemistry