Stability criterion for projective synchronization in three-dimensional chaotic systems |
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| Institution: | 1. Department of Mathematics and Statistics, University of Konstanz, Konstanz D-78464, Germany;2. Institute for Applied Research, University of Applied Sciences / HTWG Konstanz, Brauneggerstr. 55, Konstanz D-78405, Germany;1. The Institute of Mathematics, Anhui Normal University, Wuhu 241000, PR China;2. Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, Maribor SI-2000, Slovenia;3. Faculty of Natural Science and Mathematics, University of Maribor, Koro?ka c.160, Maribor SI-2000, Slovenia;4. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, Maribor SI-2000, Slovenia |
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| Abstract: | 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 σ>?1 for the Lorenz and μ>0 for the disk dynamo. |
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