Journal
NONLINEAR DYNAMICS
Volume 78, Issue 4, Pages 2331-2340Publisher
SPRINGER
DOI: 10.1007/s11071-014-1570-3
Keywords
Two-dimensional chaotic systems; The shape of chaotic attractor; Signed curvature; Shape synchronization
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Funding
- National Science Foundation of China [61273219]
- Guangdong Natural Science Foundation [S2013010015768]
- Specialized Research Fund for the Doctoral Program of Higher Education [2013-4420110003]
- KLGHEI [2013CXZDA015]
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This paper investigates the drive-response synchronization in shape for a class of two-dimensional continuous systems of chaos. The shape of the chaotic attractor of the drive chaotic system is considered in this paper. Using the signed curvatures of plane curves to describe the shapes of trajectories for drive and response systems, the continuous controller for shape synchronization is synthesized based on the fundamental theorem on plane curves in classical differential geometry. The continuous controller synthesized can guarantee that the response system is synchronized with the drive chaotic system in shape. The shape synchronization is obtained in spite of different dimensions in drive and response systems. Finally, the Duffing oscillator is utilized as an illustrative example. Simulation results show that the method proposed in this paper is effective for the application of secure communication.
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