  A simple example of a dynamical system would be the equations describing the motion of a pendulum. The equations of a dynamical system are often referred to as dynamical or evolution equations describing the change in time of variables taken to adequately describe the target system (e.g., the velocity as a function of time for a pendulum). A complete specification of the initial state of such equations is referred to as the initial conditions for the model, while a characterization of the boundaries for the model domain are known as the boundary conditions. An example of a dynamical system with a boundary condition would be the equation modeling the flight of a rubber ball fired at a wall by a small cannon. The boundary condition might be that the wall absorbs no kinetic energy (energy of motion) so that the ball is reflected off the wall with no loss of energy. The initial conditions would be the position and velocity of the ball as it left the mouth of the cannon. The dynamical system would then describe the flight of the ball to and from the wall. 