A necessary condition of projective synchronization in discrete-time systems of arbitrary dimensions

The necessary condition of projective synchronization in discrete-time systems of arbitrary dimensions is investigated. We found that the determinant of the multiplication of Jacobian matrices of the uncoupled sub-system tends to zero when projective synchronization happens. This finding also provides a theoretical explanation why the conditional Lyapunov exponent becomes null in projective synchronization, observed in the early studies.