Deterministic system

[1] A deterministic model will thus always produce the same output from a given starting condition or initial state.

In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic.

However, in practice, knowledge about the future state is limited by the precision with which the initial state can be measured, and chaotic systems are characterized by a strong dependence on the initial conditions.

A deterministic model of computation, for example a deterministic Turing machine, is a model of computation such that the successive states of the machine and the operations to be performed are completely determined by the preceding state.

Generally, for such random choices, one uses a pseudorandom number generator, but one may also use some external physical process, such as the last digits of the time given by the computer clock.

parabolic projectile motion showing velocity vector
The trajectory of a projectile launched from a cannon is modeled by an ODE that is derived from Newton's second law.