Research ArticleNeural modeling

Memristive stochastic plasticity enables mimicking of neural synchrony: Memristive circuit emulates an optical illusion

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Science Advances  25 Oct 2017:
Vol. 3, no. 10, e1700849
DOI: 10.1126/sciadv.1700849


  • Fig. 1 Schematic of temporal binding of different attributes of the same object.

    (A) A bistable image of the hippo allows the association of either the body of the hippo (labeled A) or the background (labeled B) with aspects 1 to 4 of the drawing. In (B), the background is associated to attributes 1 and 2, and in (C), those attributes are associated to the body of the hippo. (D) Attribute 3 is associated neither to the background nor to the body of the hippo. (E) Emulation of the binding process by using synchronization within an oscillator network. [A similar drawing is published by Shepard (33, 34).]

  • Fig. 2 Stochastic plasticity.

    (A) Sketch of the formation of LTP. LTP is activity-dependent, that is, it depends on the number of action potentials appearing in a time interval in the presynaptic neuron. (B) I-V curve of an Ag-doped TiO2−x–based memristive device. Inset: Simplified cross-sectional view graph. (C) Distribution of the set voltage obtained from 1700 identical voltage sweeps. The sweep rate for positive and negative voltages are 0.74 and 0.49 V/s, respectively. For the measurement, a current compliance of 0.1 mA is used. The red line is a Gaussian distribution fitted to the data. (D) Measured conductance variations of the device by applying a voltage train (see sketch in the inset) containing 1-ms voltage pulses with amplitudes of 1.1 V (blue points) and 1.3 V (red points). (E) Probability that switching from the low to high conductance state occurs for a given voltage amplitude within a pulse train, which contains 5, 10, and 50 voltage pulses. Solid lines are the prediction made by the distribution function fN(V) of Eq. 1; points are measured data. (F) Probability of emulating synaptic plasticity by the number of applied voltage pulses: For a fixed voltage pulse amplitude of 1.5 V, the probability of switching is increased from 13 to 98% (blue curve). This is associated with a decrease of θthr [voltage, where fV(V) = 0.5; Eq. 1] from 1.65 to 1.2 V (red curve).

  • Fig. 3 Two memristively coupled self-sustained oscillators with stochastic plasticity.

    (A) Illustration of two mutually coupled self-sustained oscillators with a sensory input SI. The memory is introduced by the memristive device. The conductance gM of the memristive device can be changed depending on the number of voltage pulses (applied by SI) received via SI. (B) Circuit used to implement two memristively coupled self-sustained relaxation oscillators. The circuit consists of two relaxation oscillators based on the PUT, a single memristive device, and a voltage input pulse branch VP, which accounts for the higher-level stimuli SI. (C) Voltage traces recorded at VG1 and VG2 (upper graph) and the voltage across the memristive device VM (lower graph), which increases to 2.4 V by the applied stimuli through the input SI. After the voltage stimuli, the frequency and phase synchronization of both oscillators was observed. (D) Corresponding phase portrait of the system (in gray). Some cycles of the uncoupled (in blue) and the coupled (in red) phase are highlighted. The device reset is used to uncouple the oscillators. (E) Cumulative probability of the memristive cells for the reset process obtained from 795 identical voltage sweeps. (F) Voltage traces recorded at VG1 and VG2 (upper graph) and the voltage across the memristive device VM (lower graph), which increases the device resistance back to the inertial resistance state. Thus, the oscillators are desynchronized in frequency and phase.

  • Fig. 4 Emulation of temporal binding of different attributes of the same object.

    (A and B) Sketch of the implemented circuit of six oscillators and eight memristive devices. (A) Initially, the two object oscillators (vdPA, body of the hippo; vdPB, background of the image) are not associated to one of the attribute oscillators vdP1 to vdP4. All memristive devices are in its high-resistance state (colored in orange). (B) After learning, oscillators vdP1 and vdP2 are coupled to vdPA, whereas vdP3 and vdP4 are coupled to vdPB. The corresponding memristive devices (mA1, mA2/mB3, mB4) switch to its low-resistance state (colored in green). (C) Recorded voltage traces of the six network oscillators. For the measurement, a voltage train of eight voltage pulses with an amplitude of approximately 1.8 V is used.

  • Fig. 5 Context-dependent self-organized network formations.

    Change in the input activity locally shifts the switching probability of the particular devices and the synchronization of the different oscillators. The frequencies of the network oscillators for the subnetwork configurations are shown. (A) Oscillators 1 and 2 (red curves) are bound to oscillator A (body of the hippo), whereas oscillators 3 and 4 are associated to the background (oscillator B). (B) Oscillators 3 and 4 are associated to the body of the hippo, whereas oscillator B is coupled to oscillators 1 and 2. (C) Oscillator 1 is not associated to the background or to the body of the hippo.