Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control

Abstract

The objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.

Keywords

• anti-synchronization
• adaptive control
• fractional order hyperchaos
• fractional order chaos
• unknown parameters
• 05.45.-a
• 47.52.+j
• 89.75.-k