The concept of networks has been important in the study of complex systems. In networks, links connect pairs of nodes forming complex structures. Studies have shown that networks not only contain structure but may also evolve in time. The addition of the temporal dimension adds complexity on the analysis and requests the development of innovative methods for the visualization of real-life networks. In this paper we introduce the Dynamic Network Visualization System (DyNetVis), a software tool for visualization of dynamic networks. The system provides several tools for user interaction and offers two coordinated visual layouts, named structural and temporal. Structural refers to standard network drawing techniques, in which a single snapshot of nodes and links are placed in a plane, whereas the temporal layout allows for simultaneously visualization of several temporal snapshots of the dynamic network. In addition, we also investigate two approaches for temporal layout visualization: (i) Recurrent Neighbors, a node ordering strategy that highlights frequent connections in time, and (ii) Temporal Activity Map (TAM), a layout technique with focus on nodes activity. We illustrate the applicability of the layouts and interaction functionalities provided by the system in two visual analysis case studies, demonstrating their advantages to improve the overall user experience on visualization and exploratory data analysis on dynamic networks.