Automatic speaker recognition algorithms typically characterize speech audio using short-term spectral features that encode the physiological and anatomical aspects of speech production. Such algorithms do not fully capitalize on speaker-dependent characteristics present in behavioral speech features. In this work, we propose a prosody encoding network called DeepTalk for extracting vocal style features directly from raw audio data. The DeepTalk method outperforms several state-of-the-art speaker recognition systems across multiple challenging datasets. The speaker recognition performance is further improved by combining DeepTalk with a state-of-the-art physiological speech feature-based speaker recognition system. We also integrate DeepTalk into a current state-of-the-art speech synthesizer to generate synthetic speech. A detailed analysis of the synthetic speech shows that the DeepTalk captures F0 contours essential for vocal style modeling. Furthermore, DeepTalk-based synthetic speech is shown to be almost indistinguishable from real speech in the context of speaker recognition.