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Generalized synchronization via the differential primitive element

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  • Martínez-Guerra, Rafael
  • Mata-Machuca, Juan L.

Abstract

Generalized synchronization (GS) in nonlinear systems appears when the states of one system, through a functional mapping are equal to states of another. This mapping can be obtained if there exists a differential primitive element which generates a differential transcendence basis. We introduce a new definition of GS in nonlinear systems using the concept of differential primitive element. In this contribution, we investigate the GS problem when we have strictly different nonlinear systems and we consider that for both the slave and master systems only some states are available from measurements. The first component of the mapping is called differential primitive element and, in general, is defined by means of a linear combination of the known states and the inputs of the system. Furthermore, we design a new dynamical feedback controller able to achieve complete synchronization in the coordinate transformation systems and GS in the original coordinates. These particular forms of GS are illustrated with numerical results of well-known chaotic benchmark systems.

Suggested Citation

  • Martínez-Guerra, Rafael & Mata-Machuca, Juan L., 2014. "Generalized synchronization via the differential primitive element," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 848-857.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:848-857
    DOI: 10.1016/j.amc.2014.01.142
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    1. Wang, Yan-Wu & Guan, Zhi-Hong, 2006. "Generalized synchronization of continuous chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 97-101.
    2. Liu, Hui & Chen, Juan & Lu, Jun-an & Cao, Ming, 2010. "Generalized synchronization in complex dynamical networks via adaptive couplings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1759-1770.
    3. Huang, Yuehua & Wang, Yan-Wu & Xiao, Jiang-Wen, 2009. "Generalized lag-synchronization of continuous chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 766-770.
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    1. Huang, Yuanyuan & Wang, Yinhe & Chen, Haoguang & Zhang, Siying, 2016. "Shape synchronization control for three-dimensional chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 136-145.

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