Chaos theory studies the behavior of deterministic dynamical systems that are nonetheless unpredictable due to sensitive dependence on initial conditions. Unlike linear systems—where small causes produce proportionally small effects—chaotic systems are nonlinear. Minute differences in initial states, including rounding errors in computation, can amplify exponentially, leading to radically different outcomes. This phenomenon is known as the butterfly effect, a term popularized by meteorologist Edward Lorenz to illustrate how tiny perturbations can have large-scale consequences.

Despite their apparent randomness, chaotic systems obey precise deterministic laws. A system is considered chaotic if it exhibits three defining properties: sensitivity to initial conditions, topological mixing (trajectories explore the phase space), ...