Abstract
The rationale behind dynamic models in general and in economic analysis in particular was discussed in Chaps. 14, 15, and 16. The reason for a system of difference or differential equations follows the same logic, except that here more than one dynamic process is at work and, therefore, we need more than one equation to describe these processes. Analysis of dynamic systems is a vast field of inquiry and could be the subject of a multivolume book. Here we confine ourselves to two topics that are deemed most useful for economic analysis: the solution of linear systems of homogeneous differential equations with constant coefficients and qualitative analysis of a system of differential equations using phase portrait.
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- 1.
Whereas the theory developed in this chapter is quite general and pertains to a system of two and more differential equations, for the ease and clarity of exposition, with a few exceptions, we will confine ourselves to systems of two equations.
- 2.
To obtain the Jordan canonical form one can use either normalized eigenvectors—that is, vectors of unit length—or eigenvectors of any length. In the text both normalized and nonnormalized eigenvectors are used. Normalized eigenvectors, however, are required for the radial decomposition of a positive definite matrix, discussed in Chap. 7. Note that the eig function in Matlab returns normalized eigenvectors.
- 3.
The generalized eigenvector is explained in Chap. 7.
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© 2011 Springer-Verlag Berlin Heidelberg
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Dadkhah, K. (2011). Dynamic Systems. In: Foundations of Mathematical and Computational Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13748-8_17
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DOI: https://doi.org/10.1007/978-3-642-13748-8_17
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