This paper investigates the chaotic dynamics in Hopfield neural networks (HNNs) under the influence of pulse-controlled memristors, focusing on the emergence of symmetric multi-double-scroll attractors. The study aims to explore the potential of symmetric attractors, which are more stable and diverse, in brain-like neural activities and learning. The authors propose a memristive HNN capable of generating multi-scroll attractors and introduce multi-level-logic pulses to simulate one of its parameters. The results show that the introduction of these pulses expands the original multi-scroll structure into a symmetric one, enhancing the chaotic parameter range. The correctness of the model is verified through hardware experiments, providing valuable insights for neural dynamics research and the application of memristors. The paper also reviews previous research on HNNs and memristors, highlighting the potential of memristive HNNs in generating complex dynamic behaviors.This paper investigates the chaotic dynamics in Hopfield neural networks (HNNs) under the influence of pulse-controlled memristors, focusing on the emergence of symmetric multi-double-scroll attractors. The study aims to explore the potential of symmetric attractors, which are more stable and diverse, in brain-like neural activities and learning. The authors propose a memristive HNN capable of generating multi-scroll attractors and introduce multi-level-logic pulses to simulate one of its parameters. The results show that the introduction of these pulses expands the original multi-scroll structure into a symmetric one, enhancing the chaotic parameter range. The correctness of the model is verified through hardware experiments, providing valuable insights for neural dynamics research and the application of memristors. The paper also reviews previous research on HNNs and memristors, highlighting the potential of memristive HNNs in generating complex dynamic behaviors.