Chaos in fractional-order Genesio–Tesi system and its synchronization

In this paper we study the chaotic dynamics of fractional-order Genesio–Tesi system. Theoretically, a necessary condition for occurrence of chaos is obtained. Numerical investigations on the dynamics of this system have been carried out and properties of the system have been analyzed by means of Lyapunov exponents. It is shown that in case of commensurate system the lowest order of fractional-order Genesio–Tesi system to yield chaos is 2.79. Further, chaos synchronization of fractional-order Genesio–Tesi system is investigated via two different control strategies. Active control and sliding mode control are proposed and the stability of the controllers are studied. Numerical simulations have been carried out to verify the effectiveness of controllers.

► Calculation of Lyapunov exponents for fractional-order Genesio-Tesi system.
► Necessary condition for chaos occurrence in fractional-order Genesio-Tesi system.
► The lowest order of fractional-order Genesio-Tesi system to yield chaos is 2.79.
► Synchronization fractional-order Genesio-Tesi systems via active control.
► Robust Synchronization fractional-order Genesio-Tesi systems via sliding mode control.