Simplification of Chua corsage memristor and hardware implementation of its neuron circuit

Abstract

The Chua corsage memristor (CCM) is a voltage-controlled locally-active memristor, which has complex dynamic behaviors and potential applications in the field of neuromorphic computing. According to the DC <em>V</em>-<em>I</em> plot, the CCM can be classified into two-lobe, four-lobe, and six-lobe types. By analyzing their non-volatility and local activity, we found they have the same locally-active region and a common stable equilibrium. The mathematical models of the three CCMs are simplified based on the mechanism of neuromorphic behaviors, namely, local activity. After the model simplification, the absolute value operation disappears, but the locally-active domain remains unchanged. For the simplified CCM, its small-signal equivalent circuit at the locally-active operating point has been established, which is consistent with CCMs before simplification. Hence, the model simplification does not change the small-signal characteristics of CCMs. To further investigate the application of voltage-controlled locally-active memristor in modeling the neuromorphic behavior of neurons, the simplified CCM model is used to connect a capacitor and an inductor to construct a third-order neuron circuit. By applying theoretical analysis methods such as local activity, edge of chaos, and Lyapunov exponents, we predict the parameter domains where different neuromorphic behaviors are generated. The distribution of neuromorphic behaviors is described on a dynamic map defined by the parameters of applied voltage <em>V</em><sub>D</sub> and external inductance <em>L</em>. When the memristor is biased at the locally-active region, the system response changes among resting state, periodic spiking oscillation, and chaotic behaviors. Finally, according to the simplified CCM mathematical model, the corresponding emulator circuit is designed by using three operational amplifiers, two multipliers, two current conveyors, and several resistors and capacitors. Based on the presented memristor emulator circuit, the hardware implementation of the neuron circuit is given. The experimental results verify the correctness and feasibility of the simplified CCM emulator circuit, and show that the simplified CCM-based neuron circuit can produce a variety of neuromorphic behaviors, including resting state, periodic spiking, chaotic state, bimodal response, periodic oscillation, all-or-nothing phenomenon, and spike clustering phenomenon. We expect that this work is helpful to further study the mechanism of neuromorphic behaviors of the neuron circuit and its practical applications.