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Linear observer based projective synchronization in delay Rössler system. (English) Zbl 1221.34138

Summary: A new type of linear observer based projective, projective anticipating and projective lag synchronization of time-delayed Rössler system is studied. Along with this, the approach arbitrarily scales a drive system attractor and hence a similar chaotic attractor of any desired scale can be realized with the help of a synchronizing scaling factor. A scalar synchronizing output is considered where the output equation includes both the delay and non-delay terms of the nonlinear function. The condition for synchronization is derived analytically and the values of the coupling parameters are obtained. Analytical results are verified through numerical investigation and the effect of modulated time delay in the method is discussed. An important aspect of this method is that it does not require the computation of conditional Lyapunov exponents for the verification of synchronization.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34K20 Stability theory of functional-differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93D15 Stabilization of systems by feedback
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