A research group at the University of Canterbury are developing an experimental device that may have some statistical properties in common with biological neuronal networks. Measurements of the device’s conductance have shown step change events, with evidence of correlation in the probability distribution of event-to-event intervals and also in the autocorrelation function of event times. A simulation of the device was previously developed using a probabilistic approach to modelling the internal activity. This probabilistic model was able to produce visually similar conductance behaviour but was unable to reproduce evidence of correlation.

The two main objectives of this Master’s project were to improve the simulation to produce behaviour more like the real device and also show evidence of correlation, and to develop tools to aid analysis and visualisation of simulation behaviour.

The existing probabilistic switching model was investigated and it was confirmed that it does not produce evidence of correlation in conductance step change events. Two new probabilistic models were developed by first adding gradual rather than instantaneous switching, and then implementing switching probability dependent on electric field and current, rather than fixed probability. The new models were tested and found to be unable to produce evidence of correlation, despite their differences to the original probabilistic model.

A new switching model was developed using deterministic rules based on physical processes rather than probability. The deterministic model was successful in producing evidence of correlation, for a range of configuration parameters. The conductance behaviour of the deterministic simulation was consistent with the experimental device and showed evidence of correlation in both the probability distribution of event-to-event intervals, and also in the autocorrelation function of event times. The effects of the deterministic simulation parameters (such as voltage, and dependence on electric field strength and current) were explored over ranges of values. The behaviour for each simulation was recorded and plotted, mapping trends of behaviour. It was found that for the parameters controlling the electric field strength dependence and the current dependence, there is a small range of ratios of these parameters that produce the desired behaviour. The insight gained from this mapping can be used to produce simulations that behave in a qualitatively similar fashion to the experimental device, which is a

significant achievement.

Tools were developed to aid in analysis and assessment of simulation behaviour. A script written in MATLAB analyses and plots the behaviour and statistics of simulated or experimentally measured data. Tools like this one were crucial for assessing the performance of the simulation and comparing it to the experimental device. Other scripts written in Python extract internal details of the simulated device to plot visualisations of the internal structure and conditions, or histograms of event distribution with respect to electric field and current producing those events.