Review on memristor application in neural circuit and network

Memristor is a nonlinear electronic component with memory properties, it is widely used in a variety of nonlinear circuits for extensive adaptive control and model description of neural activities. The nonlinear dynamic characteristics of the complex systems can be enhanced by adding memristive terms, which account for the high order nonlinearity in a memristor. For example, involvement of one or two memristors into branch circuits of nonlinear circuits can regulate the channel currents across capacitive and inductive components, and then the energy proportion is changed between these electronic components as well. A memristive neuron model can be obtained by introducing a memristor into the neural circuit, and the memristive current has important impact on the mode selection and stability in the neural circuit and neural activities. Based on these memristive neuron models, field coupling can be activated to control the collective behaviors of neurons even when synaptic coupling between neurons is non-valuable. Magnetic flux-controlled memristor (MFCM) and charge-controlled memristor (CCM) keep the field energy in two different forms, and they can receive or capture external field energy by regulating the currents along the memristive channels. That is, the energy flow via the memristor can control the neural circuits and nonlinear circuits coupled by memristors, and the memristive systems become controllable in adaptive way. Therefore, clarification of the energy characteristic for each electric component is crucial for setting and control of a memristive circuit and memristive neural network. Indeed, discovering the relation between a memristive oscillator and equivalent maps is a challenge and thus the reliability of memristive maps can be confirmed and explained from physical aspect, which realistic dynamical systems have distinct energy description. In this review, the basic property and its application of memristor in computational neuroscience are discussed and clarified from the physical viewpoints, the energy function is defined and adaptive control law under energy flow is proposed, field coupling between memristive systems, electromagnetic induction and radiation in cardiac tissue, application of memristive systems in the image encryption are summarized to provide possible guidance for implement of memristive systems.