Chaotic dynamics in nanoscale NbO₂ Mott memristors for analogue computing

Abstract

At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos¹ that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains^2,3,4,5,6,7. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos², and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems⁸. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos^9,10,11,12, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking^5,6,13. Here we describe niobium dioxide (NbO₂) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal–insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator¹⁴ and observe a tunable range of periodic and chaotic self-oscillations¹⁵. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.