Nonlinear methods to control synchronization between fractional-order and integer-order chaotic systems

Abstract

In this paper, we present nonlinear methods to synchronize different dimensional master and slave chaotic systems described by integer-order and fractional-order differential equations. Based on integer-order Lyapunov stability method and fractional-order Lyapunov approach, effective control schemes to rigorously study the coexistence of generalized synchronization and inverse generalized synchronization, between integer-order and fractional-order chaotic systems with different
dimensions, are introduced. Numerical examples are used to verify the effectiveness of the proposed schemes.