0000000001145752
AUTHOR
V. A. Slipko
Modeling Networks of Probabilistic Memristors in SPICE
Efficient simulation of stochastic memristors and their networks requires novel modeling approaches. Utilizing a master equation to find occupation probabilities of network states is a recent major departure from typical memristor modeling [Chaos, solitons fractals 142, 110385 (2021)]. In the present article we show how to implement such master equations in SPICE – a general purpose circuit simulation program. In the case studies we simulate the dynamics of acdriven probabilistic binary and multi-state memristors, and dc-driven networks of probabilistic binary and multi-state memristors. Our SPICE results are in perfect agreement with known analytical solutions. Examples of LTspice code are…
Switching synchronization in 1-D memristive networks: An exact solution
We study a switching synchronization phenomenon taking place in one-dimensional memristive networks when the memristors switch from the high to low resistance state. It is assumed that the distributions of threshold voltages and switching rates of memristors are arbitrary. Using the Laplace transform, a set of non-linear equations describing the memristors dynamics is solved exactly, without any approximations. The time dependencies of memristances are found and it is shown that the voltage falls across memristors are proportional to their threshold voltages. A compact expression for the network switching time is derived.
Importance of the window function choice for the predictive modelling of memristors
Window functions are widely employed in memristor models to restrict the changes of the internal state variables to specified intervals. Here we show that the actual choice of window function is of significant importance for the predictive modelling of memristors. Using a recently formulated theory of memristor attractors, we demonstrate that whether stable fixed points exist depends on the type of window function used in the model. Our main findings are formulated in terms of two memristor attractor theorems, which apply to broad classes of memristor models. As an example of our findings, we predict the existence of stable fixed points in Biolek window function memristors and their absence…