Sensitive dependence on initial conditions is a concept in chaos theory, which suggests that small differences in the starting state of a system can lead to vastly different outcomes. This means that even tiny changes in initial conditions can result in unpredictable and divergent behavior over time. A classic example of this phenomenon is the butterfly effect, where the flapping of a butterfly's wings in one part of the world could theoretically influence weather patterns elsewhere. This illustrates how interconnected systems can be, and how difficult it can be to predict long-term behavior in complex systems.