Linear Dynamical Systems
Linear dynamical systems can be solved in terms of simple functions and the behavior of all orbits classified. In a linear system the phase space is the N-dimensional Euclidean space, so any point in phase space can be represented by a vector with N numbers. The analysis of linear systems is possible because they satisfy a superposition principle: if u(t) and w(t) satisfy the differential equation for the vector field (but not necessarily the initial condition), then so will u(t) + w(t).
Read more about this topic: Dynamical System
Famous quotes containing the word systems:
“Not out of those, on whom systems of education have exhausted their culture, comes the helpful giant to destroy the old or to build the new, but out of unhandselled savage nature, out of terrible Druids and Berserkirs, come at last Alfred and Shakespeare.”
—Ralph Waldo Emerson (1803–1882)