Deterministic system (mathematics)

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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:

x(t) = v*t + {x_0}\,

where x(t) is the position at any given time, v is the velocity, t is time, and {x_0} is the initial position.

Given initial input values v and {x_0}, we can exactly predict the position of x(t) at any time in the future or the past.