Synchronization of chaotic and hyperchaotic systems

In this paper, we study the conditions under which chaotic and hyperchaotic systems can be synchronized by impulses sampled from a part of their state variables. By calculating the Lyapunov exponents of variational synchronization error systems, we show that this kind of impulsive synchronization can be applied to almost all hyperchaotic systems. We also study the selective synchronization of chaotic systems. In a selective synchronization scheme, the synchronizing signal is chosen in the time periods when the Lyapunov exponents of variational synchronization error systems are negative. Since only driving signals in the time periods when synchronization error can be reduced is chosen to reduce the synchronization error and those in the time periods when synchronization error can be increased are not used, the selective synchronization scheme can be used to achieve synchronization even in the case when continuous synchronization schemes fail to work.