A necessary condition of projective synchronization in discrete-time systems of arbitrary dimensions. (English) Zbl 1060.93535

Summary: 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.


93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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