Deterministic modeling of the diffusive memristor

Recently developed diffusive memristors have gathered a large amount of research attention due to their unique property to exhibit a variety of spiking regimes reminiscent to that found in biological cells, which creates a great potential for their application in neuromorphic systems of artificial intelligence and unconventional computing. These devices are known to produce a huge range of interesting phenomena through the interplay of regular, chaotic, and stochastic behavior. However, the character of these interplays as well as the instabilities responsible for different dynamical regimes are still poorly studied because of the difficulties in analyzing the complex stochastic dynamics of the memristive devices. In this paper, we introduce a new deterministic model justified from the Fokker-Planck description to capture the noise-driven dynamics that noise has been known to produce in the diffusive memristor. This allows us to apply bifurcation theory to reveal the instabilities and the description of the transition between the dynamical regimes.