Abstract: The synchronization of two symmetrically nonlinear-coupled hyperchaotic Rössler systems is discussed.A special nonlinear-coupled term is constructed by a suitable separation of the linear and nonlinear terms of a hyperchaotic system.The phenomenon of stable chaotic synchronization is found in a certain region around α=0.5.The stability of the synchronous state is examined by the stability criterion of linear systems and conditional Lyapunov exponent.The synchronization of the network linked by hyperchaotic Rössler systems using special nonlinear coupling function is studied.It is shown that the stability region of coupling units is expected from an estimating stability region of two coupling units only.And the coupling strength is in inverse proportion to the number of coupling units.Numerical results demonstrate that the proposed method is effective for hyper-chaotic systems and networks.

Key words: chaotic synchronization, nonlinear-coupled, stability criterion, hyperchaos, network