Abstract: The problem of full\|state hybrid projective synchronization (FSHPS) of hyperchaotic Rssler systems was studied based on Lyapunov stability theory. Adaptive control rules were proposed for Rssler hyper chaotic systems. Theoretical analysis and numerical simulation show that the controlling strategy can implement full\|state hybrid projective synchronization for the chaotic systems with different initial conditions. The paper for the first time propose the synchronization that of the hyperchaotic Rssler system when its response system also has the constant diagonal matrix 〖WTHX〗α〖WT〗 simultaneously. In this letter, we used the term “IFSHPS” (an acronymfor improved full-state hybrid projective synchronization) to distinguish the “FSHPS”. The improved FSHPS scheme was given and illustrated with hyperchaotic Rssler system as an example. The corresponding numerical simulation results were presented to verify the effectiveness of the proposed scheme.

Key words: improved full-state hybrid projective synchronization, hyperchaotic system, full-state hybrid projective synchronization, adaptive control 