Abstract
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.
Highlights
For the past decade artificial intelligence and machine learning has witnessed a huge increase in their applications and their utilization in both academia and industry, with modern machine learning methods being applied in a huge range of fields, such as financial economics2, particle physics3,4 and even autonomous vehicles5,6
Our results suggest that under certain conditions this device can demonstrate chaos-like dynamics in the statistical description, to the phenomena previously reported for ensemble of noisy oscillators55
We propose a model of the diffusive memristor where the Langevin equation describing the motion of an Ag-metallic nanocluster is replaced by its Fokker-Planck counterpart
Summary
For the past decade artificial intelligence and machine learning has witnessed a huge increase in their applications and their utilization in both academia and industry, with modern machine learning methods being applied in a huge range of fields, such as financial economics, particle physics and even autonomous vehicles. The combination of mechanical, thermal and electrical degrees of freedom allows this device to have a wide range of stochastic, dynamical and sometimes chaotic behavior (see, e.g., Ref17,18) Is this memristor interesting from a mathematical viewpoint, the device can emulate both long-term and short-term plasticity, meaning that it resembles biological cell mechanics closer than other memristive devices. “Artificial neurons” based on different memristors have been produced, of which they are seemingly capable of showing regular spiking which makes them an ideal candidate for oscillator-based computing, a new computational concept relying on accurate phase and frequency locking of synchronized oscillators This is problematic for the diffusive memristor as this device shows highly random spiking, but this may be advantageous when mimicking biological neurons where noise plays an essential role. We find that the deterministic model is capable of replicating the two main forms of spiking observed in the stochastic version, providing us with a better understanding of how to control the seemingly random spiking of stochastic diffusive artificial neurons
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