A chaotic circuit based on a physical memristor

The memristor is a fundamental two-terminal electrical component unique in that it possesses the properties of non-linearity and memory, which are pervasive across natural systems. It has been proven to be in principle a viable substrate for novel dynamical systems showing chaotic behavior, but the recourse to abstract, idealized mathematical non-linearities throughout the existing literature hinders practical realization using physical devices. In this work, we realize a fully autonomous chaotic oscillator circuit based on self-directed channel memristors. Its architecture comprises two feedback loops, a linear one and a non-linear one involving the memristor. Low-dimensional chaotic dynamics are readily obtained experimentally using tungsten-based as well as carbon-based physical devices, despite their non-idealities. A mathematical model of the circuit, revealing further interesting non-linear features such as bifurcations without parameters, is also offered.