Models that describe how things change over time are known as dynamical systems. The basic idea goes back to Newton, who showed that you can predict the movement of any physical system if you know the state of the system and the forces acting on it. In physics, the state of the system is the positions and velocities of its components, which could be planets or roulette balls. We say the dynamical system is deterministic if no randomness is involved; that is, if the state at a given instant in time precisely determines the state at the next instant. As the state evolves, it traces out a curve, called the trajectory.
Most dynamical systems have what are called attractors that determine their long-term behavior.
For exemple, due to air resistance, a pendulum will eventually come to a state of rest. This type of attractor is called a fixed point, for obvious reasons. For a slightly richer example, consider a grandfather clock, whose pendulum has a spring that keeps it moving. As long as the spring is wound, the pendulum swings back and forth at a consistent frequency; the attrator here is a pattern of oscillation, called a limit cycle, which looks like a closed loop: as the pendulum swings back and forth, a plot of its positions vs velocity traces out a circle, which it goes around again and again.