Reaction-diffusion systems are mathematical models that describe how substances spread and react over time. They involve two main processes: reaction, where substances interact and change, and diffusion, where they move from areas of high concentration to low concentration. These systems can explain various natural phenomena, such as the patterns seen in animal coats and the formation of chemical waves. In these systems, the behavior of the substances is often represented by partial differential equations. The interplay between reaction and diffusion can lead to complex patterns, such as stripes or spots, which are studied in fields like biology, chemistry, and physics.