Applying Circulant Matrices Properties to Synchronization Problems

  • Jose S. CánovasEmail author
Part of the Understanding Complex Systems book series (UCS)


In this chapter, we use circulant matrices to study discrete dynamical systems of higher dimension than one. We show how these matrices are a common framework which is useful to investigate some dynamical properties of some models provided by natural and social sciences. In particular, discrete models from Biology, Economy and Chemistry are considered and analyzed with tools coming from the properties of circulant matrices. More precisely, the special shape of eigenvalues and eigenvectors of circulant matrices is very useful to check whether the dynamics of systems on phase spaces with dimension greater than two can be reduced to that of one dimensional systems.



This work has been supported by the grants MTM2014-52920-P and MTM 2017-84079-P from Ministerio de Economía y Competitividad (Spain).


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada y EstadísticaUniversidad Politécnica de CartagenaCartagenaSpain

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