Complex dynamics is a field of mathematics that studies systems that can change in unpredictable ways. These systems often involve simple rules that can lead to intricate and chaotic behavior. For example, the behavior of a flock of birds or the patterns formed by fractals can be analyzed using complex dynamics, revealing how small changes can lead to vastly different outcomes. In complex dynamics, researchers explore concepts like chaos theory and bifurcation, which help explain how systems transition from order to disorder. By understanding these dynamics, scientists can better predict phenomena in nature, such as weather patterns or population growth, and apply these insights to various fields, including physics and biology.