A Special Hybrid Projective Synchronization in Symmetric Chaotic System With Unknown Parameter

Abstract

A novel synchronization scheme called special hybrid projective synchronization (SHPS), in which different state variables can synchronize up to same positive or negative scaling factors, is proposed in this paper. For all the symmetric chaotic systems, research results demonstrate that the SHPS can be realized with a single-term linear controller. Taking unified chaotic system with unknown parameter as an example, based on Lyapunov stability theory, some sufficient conditions and a parameter update law are derived for the implementation of SPHS, which are verified by some corresponding numerical simulations.