Dynamic analysis and reliable mechanical optimization application of ring HNN effected with a memristive neuron

Owing to their exceptional capacity to simulate biological synapses and generate complex chaotic dynamics, locally active memristor-based neural networks have become a frontier in nonlinear systems research, while their inherent randomness further provides a potential approach for reliable mechanical optimization. In this study, a ring Hopfield neural network effected with a memristive neuron (RHNN-MN) model is designed to analyze how a memristive neuron influences the ring Hopfield neural network. Moreover, the nonlinear dynamical behavior of the model as well as the application of its chaotic sequences in reliable mechanical optimization is discussed in depth. The study first constructs a locally active memristor model and analyzes both its locally active characteristics and its integration dynamics when coupled in the RHNN-MN. Subsequently, the complex dynamics phenomena such as multiple bifurcations, quasi-periodicity, and chaos of the system are investigated from the perspectives of the memristor parameters and the weights of the neural network. Simultaneously, we propose a novel chaos optimization algorithm. The experimental results demonstrate the superiority of the algorithm in solving mechanical problems, which offers theoretical reference and practical value for the design of new neural network models and mechanical optimization.