Preserving synchronization under characteristic polynomial modifications

In this article we present a methodology under which stability and synchronization of a dynamical master/slave system configuration are preserved under specific modifications made to its Jacobian matrix's characteristic polynomial. We propose to modify the coefficients of the associated characteristic polynomial by calculating their value to the m-th power, with m an odd, positive integer. The objective is to show that under these modifications, hyperbolic critical points are preserved along the stable and unstable manifolds. It is also shown that a consequence of this approach is the preservation of the signature of the Jacobian matrix associated with the dynamical system. To illustrate the results we present several examples of well known chaotic attractors.