To detect the early developmental stages of arteriovenous access (AVA) stenosis in hemodialysis patients, this study explored a stenosis detector based on the Burg method and the fractional-order chaos system (FOCS). The bruit developed by the blood flowing through AVA can be a viable noninvasive strategy for monitoring AVA functions. We used the Burg method of the autoregressive model to estimate the frequency spectra of phonographic signals recorded by an electronic stethoscope in patients' AVAs and to identify the spectral peaks in the region of 25-800 Hz. The frequency spectra differed significantly between normal and stenosis statuses in AVA. We found that the frequency and amplitude in power spectra analysis varied in accordance with the severity of AVA stenosis. However, the correlation of these parameters for classifying the degree of stenosis is limited when only using the Burg method. Therefore, we used an FOCS to monitor the differing frequency spectra between the normal condition and AVA stenosis. The variances of these two conditions were dynamic errors that were the coupling variables that tracked the responses between the master system and the slave system. A total of 42 patients who had received percutaneous transluminal angioplasty (PTA) for their failing AVAs was recruited for this study. In this study, the dynamic error, Index Ψ, was used to calculate the frequency spectrum redistribution in patients undergoing PTA. In addition, ΔImp was the index used to evaluate improvements in the luminal diameter between pre- and post-PTA. Therefore, we used linear regression to model the relationship between ΔImp and Index Ψ. The findings indicate that the proposed method has enhanced efficiency, especially in the venous anastomosis (V-site). The FOCS is a novel and simple algorithm for analyzing the residual AVA stenosis of PTA treatment.