**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 systems**are a special type of

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**Linear**systems can also be used to understand the qualitative behavior of general

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