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Stability criterion for projective synchronization in three-dimensional chaotic systems. (English) Zbl 0983.37036

Summary: Projective synchronization, in which the state vectors synchronize up to a scaling factor, has recently been observed in coupled partially linear chaotic systems (Lorenz system) under certain conditions. In this Letter, we present a stability criterion that guarantees the occurrence of the projective synchronization in three-dimensional systems. By applying the criterion to two typical partially linear systems (Lorenz and disk dynamo), it shows that only some parameters play the key role in influencing the stability. Projective synchronization only happens when \(\sigma>-1\) for the Lorenz and \(\mu>0\) for the disk dynamo.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
86A25 Geo-electricity and geomagnetism
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