Dynamic systems are mathematical models that describe how a system evolves over time. They can be found in various fields such as physics, engineering, and economics, where they help in understanding complex behaviors and predicting future states based on current conditions. These systems can be linear or nonlinear, with nonlinear systems often exhibiting chaotic behavior. By studying dynamic systems, researchers can gain insights into stability, control, and the overall dynamics of systems, making them essential for advancements in technology and science.