**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*).

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Linear Dynamical System

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**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 approximating it as a**linear**...### Famous quotes containing the word systems:

“Our little *systems* have their day;

They have their day and cease to be:

They are but broken lights of thee,

And thou, O Lord, art more than they.”

—Alfred Tennyson (1809–1892)

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