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
Other articles related to "linear dynamical systems, dynamical system, system, linear, dynamical systems":
... Linear dynamical systems are a special type of dynamical system where the equation governing the system's evolution is linear ... While dynamical systems in general do not have closed-form solutions, linear dynamical systems can be solved exactly, and they have a rich set of mathematical properties ... Linear systems can also be used to understand the qualitative behavior of general dynamical systems, by calculating the equilibrium points of the system and ...
Famous quotes containing the word systems:
“What is most original in a mans nature is often that which is most desperate. Thus new systems are forced on the world by men who simply cannot bear the pain of living with what is. Creators care nothing for their systems except that they be unique. If Hitler had been born in Nazi Germany he wouldnt have been content to enjoy the atmosphere.”
—Leonard Cohen (b. 1934)