Système dynamique et chaos.

Abstract

This work draws new results on stabilization and on some types of synchronization applied to chaotic systems when the parameters are unknown. First, we build an adaptive controller to stabilize the chaotic system with a line of equilibria with unknown parameters towards its originally unstable equilibrium. Next, we build adaptive controllers to synchronize and antisynchronize two identical chaotic systems of the same type as the previous system. Finally, the corresponding adaptive controllers to realize generalized synchronization and modified projective synchronization are also constructed for the different chaotic systems represented by the Rossler system and its modification. Lyapunov stability theory and adaptive control theory were applied to prove all the stabilization and synchronization results derived from this work. Numerical simulations were presented to illustrate the main results.