Parkinson's disease (PD) is considered to be the second most common neurodegenerative disease which affects the patients' life throughout the years. As a consequence, its early diagnosis is of major importance for the improvement of life quality, implying that the severe symptoms can be delayed through appropriate clinical intervention and treatment. Among the most important premature symptoms of PD are the voice impairments of articulation, phonation and prosody. The objective of this study is to investigate whether the voice's dynamic behavior can be used as possible indicator for PD. Thus in this work, we employ the recurrence plots (RPs) which derive from the analysis of the three modulated vowels /a/, /e/ and /o/, which belong to the PC-GITA dataset, and are fed as input images to a 3-channel Convolutional Neural Network-based (CNN) architecture, which, finally, differentiates the 50 PD patients from 50 healthy subjects. The experimental results obtained provide evidence that the RP-based approach is a promising tool for the recognition of PD patients through the analysis of voice recordings, with a classification accuracy achieved equal to 87%.