Synchronization and Coupling Dynamics in Memristive Homogeneous and Heterogeneous Hopfield Neural Networks

In this paper, by taking a locally active memristor (LAM) as the neuronal synapse to link two identical/disparate ReLU-type Hopfield neural networks (RHNNs), the memristive homogeneous and heterogeneous neural networks are presented and their coupling dynamics are discussed in succession. The homogeneous RHNN model consists of two 3D RHNNs with a LAM, in which the coupling strength-and initial value-induced synchronous transitions are revealed. Besides, the heterogeneous RHNN model is focused on which is constructed by using a LAM to couple a 3D and 2D RHNN, where complex and rich dynamics are revealed in numerical, including hyperchaos, chaos, quasi-period, and multi-stable patterns. Particularly, attractor control of offset boosting as well as color image encryption application are realized, indicating the high controllability and security of the LAM-coupled neural networks. Finally, the electrical neuron depending on the digital circuit is implemented and hardware experimental results verify the numerical measurements well.