Multi time-delay fuzzy dispersion network analysis of nonlinear time series

The use of complex network analysis is crucial for analyzing nonlinear time series data. Unlike traditional methods, complex networks not only improve data visualization but also reveal hidden patterns and structures. However, current network construction methods often oversimplify node transformations, which can lead to susceptibility to noise and overlook important structural characteristics. To overcome this limitation, we introduce fuzzy membership functions based on recent developments in dispersion network (DN), forming a fuzzy dispersion network (FDN). By employing fuzzy membership function instead of absolute mapping, FDN quantifies node division uncertainty, thus enhancing the network's information representation. Expanding on FDN, we also present the multi time-delay fuzzy dispersion network (MTFDN), which generates intricate networks from the initial series at varying time-delays, providing multiple viewpoints for time series analysis. Ultimately, by integrating transition entropy values to depict network complexity, we accomplish efficient nonlinear time series analysis. Subsequent simulated experiments, comparing two types of noise and three types of chaotic models, demonstrate MTFDN's stability and low sensitivity to series length changes in nonlinear time series analysis. Furthermore, experimental results, conducted on four classes of ships and five types of bearing statuses, confirm that MTFDN outperforms multi time-delay DN and other methods in practical applications.