A discrete memristive heterogeneous Hopfield neural network with multi-penguin-like/silkworm-like attractors and its application in secure communication

The activation function is one of the extremely crucial components of an artificial neural network. It not only provides the neural network with nonlinear capability, but also enhances its expressive power. However, discrete neural networks with multi-attractors consisting of different activation functions have not yet been uncovered. In this work, a discrete memristive Hopfield neural network with heterogeneous activation functions and multi-penguin-like/silkworm-like attractors is proposed. The discrete memristor is used as a synapse to mimic activity between neurons with heterogeneous activation functions. Theoretical analysis and numerical simulation reveal that the system can generate various multi-penguin-like/silkworm-like attractors, and exhibit complex dynamical behaviors, including transient chaos, attractor evolution, homogeneous and heterogeneous coexisting attractors, and initial offset behavior. Meanwhile, bi-parameter dynamic results demonstrate the proposed system’s hyperchaotic and high spectral entropy properties. Furthermore, a hardware platform is designed to verify the validity and feasibility of the proposed system by adopting FPGA. Finally, the randomness of the system-generated sequences is assessed, and a secure communication scheme is presented based on the discrete memristive heterogeneous Hopfield neural network. The experimental results indicate that the proposed model performs better than existing chaotic maps.