Modified function projective bursting synchronization for fast–slow systems with uncertainties and external disturbances

Abstract

This paper addresses the modified function projective bursting synchronization (MFPBS) for a class of fast-slow systems with uncertainties and external disturbances. By using an active sliding mode control method (SMC), bursting synchronization can occur between two different chaotic systems. An active SMC law is established to guarantee uncertainties and disturbances rejection and realize the MFPBS. The sufficient condition is drawn for the stability of error dynamics, where the controllers are designed by using the relevant variables in fast-slow systems. More interestingly, more complex bursting oscillations such as chaotic bursting, as well as chaotic or periodic spiking can be obtained in slave systems with free scales when the MFPBS is maintained. And the corresponding numerical simulation is provided to illustrate the effectiveness of the proposed method.