How does chaos theory explain the behavior of complex systems, and what are its applications in various fields such as meteorology, economics, and biology?

Chaos theory studies the behavior of deterministic nonlinear systems that exhibit sensitive dependence on initial conditions, leading to unpredictable outcomes known as chaos. It provides mathematical tools for understanding complex phenomena such as turbulence, population dynamics, and stock market fluctuations, offering insights into the underlying patterns and structures of seemingly random processes and informing predictive models and decision-making strategies in diverse fields.