A memristor SPICE model accounting for synaptic activity dependence

Abstract

In this work, we propose a new memristor SPICE model that accounts for the typical synaptic characteristics that have been previously demonstrated with practical memristive devices. We show that this model could account for both volatile and non-volatile memristance changes under distinct stimuli. We then demonstrate that our model is capable of supporting typical STDP with simple non-overlapping digital pulse pairs. Finally, we investigate the capability of our model to simulate the activity dependence dynamics of synaptic modification and present simulated results that are in excellent agreement with biological results.

Fig 1. Schematic of the proposed memristor SPICE model.

Parameters utilized in simulations are: R _on = 1Ω, R _off = 100kΩ, R _init = 5kΩ, ε = 10⁶, C _x = 5mF, R _x = 1Ω, C _y = 0.15F, C _z = 1F, R _z = 3mΩ, C _w = 1F, R _w = 0.35Ω, B ₊ = −B ₋ = 0.35nV, k = 0.33e¹⁰, α = 0.706, β = 1e⁸, γ = 2, p = 0.5, j = 2 and m = 0.62. The initial condition of four internal variables are set as x ₀ = y ₀ = (R _off − R _init) / (R _off − R _on), and z ₀ = w ₀ = 0.

Fig 2. Memristor model behaviour.

(a) Simulated pinched hysteresis I-V responses at frequencies of ω₀ and 10ω₀. (b) Corresponding memristance as a function of applied voltage.

Fig 3. (a) Modelled normalized volatile conductance (G(t) = 1 / R _mem(t)) dynamics in response to three consecutive pulses possessing varying inter-pulse intervals: 2.5ms (red line) and 5ms (blue line), respectively.

For both cases, pulse amplitude and width were fixed at 4V, 10μs and the system remains fully volatile. (b) Transition from volatile to non-volatile dynamics due to a change in pulse width (10 μs to 20μs). (c) Transition from volatile to non-volatile dynamics due to a change in pulse amplitude (4V to 6V).

Fig 4. (a) Pulse pair stimulation paradigm.

A, t _width, and t _gap represent pulse magnitude, width, and inter-pulse interval. For all bipolar pulse pair-based simulations, we use m = 1 in function ϕ of module V. All other parameters were kept same as previously stated values. (b) and (c) Simulated STDP results for varying stimulus width and amplitude. (d) STDP results for varying R _z values indicating different decay constants of the STDP curve with increasing inter-pulse interval.

Fig 5. (a) Two individual driving effort sub-modules responding for only positive and only negative inputs respectively.

The overall drive effort variable v _z equals the sum of v _z+ and v _z−. (b) and (c) Asymmetric STDP curves attained by employing different resistance values in the two driving sub-modules and modifying bipolar threshold values (B ₊ = 0.31nV, B ₋ = −0.27nV) to compensate for STDP curve drift. Inset: Corresponding STDP curves with original bipolar threshold values (B ₊ = −B ₋ = 0.35nV).

Fig 6. (a) Scheme of 60 repeated pulse pairs.

In each pulse pair, the pulse parameters were set as A = 2V, t _width = 10μs, and t _gap = ±3ms for pre-post and post-pre pairs respectively. (b) Dependence of overall conductance modification after application of the input pulse pair train on pulse pair frequency.