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Criteria for the occurrence of projective synchronization in chaotic systems of arbitrary dimension. (English) Zbl 1001.37026

Summary: The conditions of projective synchronization in partially linear chaotic systems of arbitrary dimension are studied. We find that, for any bounded Jacobian matrix \(M\), projective synchronization happens when all the Lyapunov exponents are nonpositive. Several simple criteria are explored for matrix \(M\) with the properties of \(m_{ik}=m_{ki}\) and \(m_{ik}=-m_{ki}\), which enable us to assess the possibility of the synchronization by the eigenvalues and the diagonal elements of the Jacobian. All conditions are globally stable. Examples are provided to illustrate projective synchronization in high dimension.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C60 Qualitative investigation and simulation of ordinary differential equation models
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