Grid multi-double-scroll attractors in a magnetized Hopfield neural network with a memristive self-connection synapse

Grid multi-scroll attractors possess distinctive properties in complex topologies and functions, yet their generation mechanisms in the neural networks still need further exploration. This paper presents a novel method to generate the grid multi-double-scroll attractors within the neural networks. Firstly, a new magnetized Hopfield neural network (HNN) model under the influence of electromagnetic radiation is developed. This model utilizes an electromagnetic radiation control method based on a multi-piecewise memristor to efficiently regulate the number of single direction multi-double-scroll attractors. Secondly, the above proposed magnetized HNN model combined with a memristive self-connection synapse is constructed by using another multi-piecewise memristor to simulate the autapse of a neuron. This combined HNN model with the double multi-piecewise memristors demonstrates the grid multi-double-scroll attractors and the initial-offset behaviors. Finally, the feasibility of the proposed magnetized HNN model is verified by the FPGA platform.