Chaos theory models how a population of living creatures changes from one generation to the next, when there are limits to the available resources. It is one of the simplest equations that can generate deterministic chaos—apparently random behavior with no random cause. Chaos theory led us to realize that simple nonlinear equations can create very complex dynamics and that apparent randomness may conceal hidden order. Popularly known as Chaos Theory, this discovery has innumerable applications, including the motion of the planets in the solar system, weather forecasting, population dynamics in ecology, variable stars, earthquake modeling, and efficient trajectories for space probes.
Black-Scholes equation says how the price of financial derivative changes over time, based on the principle that when the price is correct.