**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":

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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 ...

**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**system around each such point ...

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