Linear systems

In modeling and simulation, an assumed state of the system under study. While most physical and social systems are actually non-linear, mathematical models and simulations of those systems usually use linear assumptions. The linear approximation is made because linear equations are simpler to handle mathematically, and over vast regions of operation the linear models provide a good match with reality. Linear systems can be stable (that is, when perturbed, the system settles to some stable value), can oscillate (that is, when perturbed, the system settles into a periodic cycle), or can be unstable (that is when perturbed, the system movements become very large and continually increase or decrease). When the systems are non-linear, as in real life, a fourth state of behavior can be triggered: chaos. In this state, the system appears to be operating in random fashion, generating noise or what appears to be noise. In this state, the system behavior is still deterministic but essentially unpredictable.