Neuron circuit made of a single locally-active memristor

Neuromorphic computing, inspired by the human brain's architecture, is expected to break the physical limits of transistors and von Neumann bottleneck. The multiple internal state variables of higher-order memristors (second-order or above) possess dynamic complexity and adaptability, enabling them to mimick the characteristics of biological neurons, which are very important building blocks for neuromorphic computing. This paper presents a simple neuron circuit containing a single second-order current-controlled locally-active memristor (LAM). The pinched hysteresis loop and DC V-I curve of the proposed second-order LAM show good odd symmetry. Applying small signal analysis method, we obtain the small-signal equivalent circuit of the neuron circuit, showing a LC parallel structure and an edge of chaos kernel in its locally-active domain. Also, we draw a parameter classification of the neuron circuit, showing four symmetrical edge of chaos domains, which plays an important role in biphasic action potentials. Finally, we demonstrate that the simple neuron circuit can produce monophasic action potentials, biphasic action potentials and co-existing neuromorphic phenomena via subcritical Hopf bifurcation with different input, verifying the simple circuit is suitable as artificial neurons.