Preservation of synchronization in dynamical systems via lyapunov methods

In this paper, we use, extend and apply some classic results of the theory of dynamical systems to study the preservation of synchronization in chaotical dynamical systems via Lyapunov method. The obtained results show that synchronization can be preserved after a particular class of changes are made to the linear part of the dynamical system. For illustrative purposes we apply a compound control law to achieve synchronization in a master-slave system. We also show that it is possible to preserve partial synchronization when an additive perturbation is included in the control law. We present numerical simulations to show the effectiveness of our method.