Multi-stable states and synchronicity of a cellular neural network with memristive activation function

The cellular neural network (CNN) is an implementable solution for fully connected neural networks. Using nanoscale memristor to realize its nonlinear activation function can simplify the circuit implementation of CNN effectively. This paper presents a paradigm of the basic CNN cell by introducing a voltage-controlled memristor as the activating module of its output circuit. A three-cell memristor-based CNN (mCNN) is constructed to demonstrate the parameter- and initial condition-influenced dynamical behaviors induced by the activating memristor. Furtherly, two identical three-cell mCNNs are chosen as the subnets to construct a memristor-coupled mCNN, based on which the multi-stable states and the synchronous behaviors are investigated. Numerical results show that the multi-stable states of the memristor-coupled mCNN are flexibly switched by adjusting the coupling strength and initial conditions. Under the control of the memristor coupler, the two subnets can achieve complete synchronization, lag synchronization and phase synchronization. Finally, the FPGA-based hardware experiments are executed to verify the numerical results.