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Projective synchronization in multiple modulated time-delayed systems with adaptive scaling factor. (English) Zbl 1215.34088
Summary: We propose a nonlinear observer-based stable synchronization in multiple time-delayed systems where the response system states are scaled replicas of the drive system states. It is very difficult to estimate the scaling factor because its dependent on the initial condition and the underlying chaotic dynamics. Based on the nonlinear observer approach, a new adaptive law is proposed to simultaneously estimate the scaling factor and projective synchronization in multiple modulated time-delayed systems. As an example, numerical simulations for the multiple time-delayed Ikeda and Mackey-Glass systems are conducted, which is in good agreement with the theoretical analysis.

MSC:
34K20 Stability theory of functional-differential equations
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