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Stability analysis for the synchronization of chaotic systems with different order: application to secure communications. (English) Zbl 1161.94389
Summary: The synchronization of different order systems or reduced-order synchronization is studied. We show that dynamical evolution of second-order oscillators can be synchronized with the canonical projection of a fourth-order chaotic system. In this sense, it is said that synchronization is achieved in reduced order. The proposed strategy is an input-output control scheme which comprises an uncertainty estimator and an exponential controller. In this way, the reduced-order synchronization is attained at any prescribed speed in spite of master/slave mismatches. Simulation results are provided to verify the operation of the designed synchronization scheme. The proposed controller is implemented to secure communication.

MSC:
94A60 Cryptography
37N99 Applications of dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D20 Stability of solutions to ordinary differential equations
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