Dynamic analysis, stabilization and synchronization of novel chaotic fractional orders systems

Abstract

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.