# Deterministic system (mathematics)

A deterministic system is a system where the inputs completely determine the system's future states; there is no randomness in producing the future state. If a deterministic system model is given initial inputs A and B, the model will produce the same states every time.

A very simple example would be a position function:

where x(t) is the position at any given time, v is the velocity, t is time, and is the initial position.

Given initial input values v and , we can exactly predict the position of at any time in the future or the past.