Memristive neurons on edge of chaos: rich neuromorphic behaviors via Hopf bifurcations

The memristor, characterized by its distinctive integration of storage and computing functionalities, has emerged as a candidate device for fostering efficient neuromorphic computing. The research into the neuromorphic dynamics of locally active memristor (LAM) is crucial for advancing neuromorphic computing. This paper proposes a new voltage-controlled LAM based on Chua Corsage Memristor (CCM) and analyzes its local activity, edge of chaos and other dynamic characteristics. According to the theories of local activity and the edge of chaos, we design a second-order neuron and a third-order neuron based on the proposed memristor, and analyze their neuromorphic dynamics under the edge mechanism. The designed third-order neuron operating at the edge of chaos is capable of generating 24 kinds of neuromorphic behaviors, including periodic and phasic spiking, bursting, self-sustained oscillations and chaos, demonstrating that a single third-order memristive neuronal circuit can achieve the switching of different spike firing patterns.