Physiological time series, such as electrocardiogram (ECG) and electroencephalogram (EEG) data, are instrumental in capturing the critical dynamics of biological systems, including cardiovascular behavior and neural activity. The traditional permutation entropy (PE) methods effectively analyze the complexity of such signals but often overlook amplitude variations, which encode essential information about physiological states and pathological conditions. This paper introduces amplitude-sensitive permutation entropy (ASPE), a novel method that enhances PE by integrating amplitude information through the coefficient of variation as a weighting factor. Unlike the existing approaches that may overemphasize or underutilize amplitude changes, ASPE's balanced weighting strategy captures both the average level and dispersion of data, preserving the overall signal complexity. To validate ASPE's effectiveness, we conducted simulation experiments and applied them to two real-world datasets: an EEG dataset of epileptic seizures and an ECG dataset of arrhythmias. In simulations, ASPE demonstrated superior sensitivity to amplitude changes, outperforming the five existing PE methods in identifying dynamic variations accurately. In the physiological datasets, ASPE distinguished disease states more effectively, accurately identifying seizure phases and arrhythmic patterns. These results highlight ASPE's potential as a robust tool for analyzing physiological data with complex amplitude dynamics, offering a more comprehensive assessment of signal behavior and disease states than the current methods.