Abstract
Resistor networks are crucial in various fields, and solving problems on these is challenging. Existing numerical methods often suffer from limitations in accuracy and computational efficiency. In this paper, a structured zeroing neural network (SZNNCRN) for solving the mathematical model of time-varying cobweb resistance networks is proposed to address these challenges. Firstly, a SZNNCRN model is designed to solve the time-varying Laplacian equation system, which is a mathematical model representing the relationship between voltage and current in a cobweb resistance network. By leveraging the hidden structural attributes of a Laplacian matrix, the study devises optimized algorithms for the neural network models, which markedly improve computational efficiency. Subsequently, theoretical analyses validate the model's global exponential convergence, while numerical simulation results further corroborate its convergence and accuracy. Finally, the model is applied to calculate the equivalent resistance within a cobweb resistive network and for path planning on cobweb maps.