Bayesian inference reveals hidden dynamics in memristive neuron models and transitions from deterministic stability to stochastic variability

• Bayesian methods are applied to uncover hidden parameters and quantify uncertainty. • Stochastic terms are introduced to reveal divergence from deterministic trajectories. • Statistical analysis is used to characterize long-term model behavior. • It is shown that insights reveal a delicate interplay between stability and randomness in memristive neurons. • A trajectory comparison is given to highlight the sensitivity to initial conditions. In this work, the underlying dynamics of a model of memristive neurons which combine memory and nonlinearity are discovered. First, in order to simplify the probabilistic understanding of the model structure, a Bayesian technique is used to model hidden parameters within a deterministic framework. Bayesian approaches offer a structured approach to measure uncertainty and improve the readability of complex models by comparing prior and posterior distributions. To highlight the impact of randomness, a stochastic factor is added to the underlying uncertainties of the models. To demonstrate how stochastic and deterministic systems follow different courses and how sensitive they are to initial conditions, trajectories are discussed. Finally, the long-term behavior of both models is shown by analysis of the statistical distribution. In addition to providing knowledge about noisy computation in biological systems where determinism and randomness coexist, these findings improve the understanding of the memristive neuron model. The findings provide information on how the memristive neuron function combines deterministic stability and stochastic unpredictability, which has implications for our understanding of brain computing.