# What does the term 'hyperbolic model' mean?

I am reading this non-linear discrete dynamical system paper. The authors mention the term hyperbolic model. What does that mean?

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## 2 Answers

I suppose it is related to hyperbolic partial differential equations.

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Example of a hyperbolic system, the first order wave equation: ${\partial \underline{U} \over \partial t} + \underline{A} {\partial \underline{U} \over \partial x} = 0$

The term hyperbolic means that:

• The eigenvalues of the $m \times m$ Jacobian matrix ($\underline A$) are all real
• There is a corresponding set of $m$ linearly independent eigenvectors

This allows decomposition of the system into a linear combination of these eigenvectors, where the corresponding eigenvalues of $\underline{A}$ give the wave speeds.

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