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Preserving synchronization under matrix product modifications

Author

Listed:
  • Becker-Bessudo, Dan
  • Fernandez-Anaya, G.
  • Flores-Godoy, J.J.

Abstract

In this article we present a methodology under which stability and synchronization of a dynamical master/slave system configuration are preserved under modification through matrix multiplication. The objective is to show that under a defined multiplicative group, hyperbolic critical points are preserved along the stable and unstable manifolds. The properties of this multiplicative group were determined through the use of simultaneous Jordan decomposition. 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 different modified systems.

Suggested Citation

  • Becker-Bessudo, Dan & Fernandez-Anaya, G. & Flores-Godoy, J.J., 2008. "Preserving synchronization under matrix product modifications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6631-6645.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:26:p:6631-6645
    DOI: 10.1016/j.physa.2008.08.016
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