Dynamics of asteroidal Hopfield neural network under electromagnetic radiation and its application in the mechanical optimization design

When the neurons of the human brain transmit information through electrical and chemical signals, they will show a complex chaotic phenomenon if they are stimulated externally. Unlike the circular or fully connected Hopfield neural network models that are currently widely studied, this paper introduces a novel four-dimensional asteroidal Hopfield neural network (AHNN) model. The AHNN model incorporates a significant number of intentionally omitted synaptic weights in its architecture, making it more closely resemble the phenomenon of partial neuronal disconnection observed in real biological networks. This design enables the model to more accurately simulate the adaptive capacity of the brain’s neural architecture, aiding in understanding the AHNN’s ability to retain functionality amid partial structural damage and exploring how such changes affect the network’s overall dynamics and stability. Besides, a memristor is used to simulate the effect of electromagnetic radiation on the network. The AHNN exhibits typical steady state or periodic state without external stimulus. When the electromagnetic radiation stimulation simulated by the memristor is added, the network exhibits various nonlinear dynamic behaviors, including but not limited to single-period, multi-period, chaos and transient chaos, which shows that electromagnetic radiation plays a significant role in regulating the dynamic behavior of neural networks. At this point, due to the need to transfer information between neurons, the synaptic weights between neurons change, which will also affect the dynamic behavior of AHNN. Based on this AHNN, a chaotic optimization algorithm was designed and applied to the mechanical optimization design problem of tension and compression springs and pressure vessels. Through the simulation of this problem and the comparison of the experimental results with some famous algorithms, the superiority of AHNN in solution quality was proved, providing a new biologically inspired idea for engineering optimization.