Geodesic
Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium
Kybernetika, Tome 49 (2013) no. 2, pp. 359-374.

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By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronized between the extended Sprott E system and original Sprott E system. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
Classification : 34D06 34H10 34H20 34C28 34D08 34C23 93C40 37D45, 34H10, 34H20, 93C40
Keywords: chaotic attractors; stable equilibrium; Shilnikov theorem; Lyapunov exponent; synchronization 
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     author = {Wei, Zhouchao and Wang, Zhen},
     title = {Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium},
     journal = {Kybernetika},
     pages = {359--374},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2013},
     mrnumber = {3085401},
     zbl = {1276.34043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_2_a9/}
}
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Wei, Zhouchao; Wang, Zhen. Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium. Kybernetika, Tome 49 (2013) no. 2, pp. 359-374. http://geodesic.mathdoc.fr/item/KYB_2013__49_2_a9/