A simple time-delay memristor and its application in 2D HR neuron model

Since the concept of memristor was proposed, the memristor, as the fourth-generation electronic component, has attracted great attention from researchers. Memristors can be used not only for nonvolatile memory but also to mimic the behavior of nervous system. The inherent nonlinearity of memristor makes it valuable in nonlinear circuits. Since it is still difficult to realize the commercial application of memristors at present, designing suitable memristor models can play a guiding role in practical application. This work proposes a novel memristor model with a time-delay state variable. The proposed memristor cannot only generate pinched hysteresis loop under periodic signal excitation, but also can generate chaotic current or even hyperchaotic current under DC voltage. The nonlinear dynamics of the proposed time-delay memristor are studied by phase portraits, bifurcation diagram and Lyapunov exponents. Furthermore, the proposed memristor is used in the HR neuron model to study neuronal electrical activities with electromagnetic induction. Multiple firing patterns of the memristive neuron can be generated such as periodic, bursting and chaotic. Finally, the memristor emulator circuit and the HR neuron model circuit are designed and simulated by Pspice.

Automated summary

Since the proposal of the concept of memristor, which is considered as the fourth-generation electronic component, it has gained significant attention from researchers due to its potential applications in nonvolatile memory and mimicking the behavior of nervous system. The inherent nonlinearity of memristor makes it valuable in nonlinear circuits, although commercial applications are still challenging. Designing suitable memristor models can guide practical applications effectively. The novel memristor model with a time-delay state variable proposed in this work exhibits interesting properties such as generating pinched hysteresis loop under periodic signal excitation and chaotic current under DC voltage, along with applications in neuronal models for studying electrical activities.