Preservation of hyperbolic equilibrium points and synchronization in dynamical systems

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 determines if the system is stable or unstable. In this work, we establish the sufficient conditions to preserve the structure of this hyperbolic points. Also, control tools are used to achieve synchronization in dynamical systems. Numerical simulations to very the effectiveness of the method are presented.