Robust adaptive modified function projective synchronization of different hyperchaotic systems subject to external disturbance

Robust adaptive modified function projective synchronization between two different hyperchaotic systems is investigated, where the external uncertainties are considered and the scale factors are different from each other. The synchronization criterion is presented, which can be realized by adaptive feedback controller with compensator to eliminate the influence of uncertainties effectively. The update laws of the unknown parameters are given and the sufficient conditions are deduced based on stability theory and adaptive control. And some mistakes in the previous works are pointed out and revised. Finally, the hyperchaotic Lü and new hyperchaotic Lorenz systems are taken for example and the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

► We study the robust adaptive modified function projective synchronization of a class of hyperchaotic systems.
► Based on stability theory, an adaptive law is derived and an compensator is introduced to adapt the uncertainties of the response systems.
► Numerical simulations verify the effectiveness of the scheme.