Design and analysis of a memristive Hopfield switching neural network and application to privacy protection

This paper considers the problem of making Hopfield neural networks (HNNs) generate multi-scroll chaotic attractors (MSCAs) and applying them to privacy protection. To this end, based on HNNs and memristors, a memristive Hopfield switching neural network (MHSNN) is constructed. Firstly, two memristive Hopfield neural networks (MHNNs) are combined into an MHNN with switching topology by designing a weight-switching mechanism. Then, a bias-switching mechanism is designed subsequently according to the states of the neurons, thereby constructing the MHSNN. It is found that the designed switching functions enable the MHSNN to generate 8-to-12-16-20-scroll chaotic attractors. The dynamics analyses verify the existence of the MSCAs, it also exhibits two interesting dynamics phenomena: (1) the number and distribution of the scrolls correspond to the number and the location of the unstable index-2 saddle-focuses (USFs-2); (2) the number of branches in the bifurcation diagrams is half of the number of the scrolls. Moreover, the digital circuit of the MHSNN is designed and verified with the help of a field programmable gate array (FPGA), and the experimental results are displayed on an oscilloscope. Finally, due to the fact that the constructed MHSNN can generate chaotic sequences with higher randomness, an MHSNN-based image encryption scheme is proposed, some comparisons with existing methods verify that the proposed encryption scheme has the advantages of fast operation and easy implementation.