Résumé:
The objective of this thesis is to study the stabilization and
synchronization of new chaotics fractionals systems, where we
proposed chaotic fractional systems in Caputo sense. We have
demonstrated that the behavior of these systems is chaotic using
the exponents of Lyapunov and confirmed their behavior using the
0-1 test. The stability and synchronization of the proposed systems
have also been studied using the adaptive control method which
depends on the change of the chaotic system parameters at each
moment. We adopted during our solution to the fractional
differential equations on the Adams Bashfort Moulton method. In
order to confirm the physical presence of the proposed chaotic
systems, we drew the electronic circuits representing them using
the Multisim program and compared the results obtained with
those from numerical simulations.
