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Robustness and preservation of stability and synchronization in the presence of structural changes is an important issue in the study of chaotic dynamical systems. In this work we present a methodology to establish conditions for preservation of stability in dynamical system in terms of linear matrix polynomial evaluation. The idea is to construct a group of dynamical transformations under which stability...
Classic results of the dynamical systems theory are extended and used to study the preservation of synchronization in chaotical dynamical systems. This results show that synchronization can be preserved after changes are made to the linear part of the dynamical system. When the Jacobian matrix of the system is evaluated in the hyperbolic points, the sign structure of the eigenvalues of this matrix...
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