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Research Papers

A Special Hybrid Projective Synchronization in Symmetric Chaotic System With Unknown Parameter

[+] Author and Article Information
Hong-juan Liu

Software College,
Northeastern University,
No. 3-11, Wenhua Road, Heping District,
Shenyang 110819, China
e-mail: liuhj@swc.neu.edu.cn

Hai Yu

Software College,
Northeastern University,
No. 3-11, Wenhua Road, Heping District,
Shenyang 110819, China
e-mail: yuhai@126.com

Zhi-liang Zhu

Software College,
Northeastern University,
No. 3-11, Wenhua Road, Heping District,
Shenyang 110819, China
e-mail: zhuzl@swc.neu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 25, 2016; final manuscript received April 9, 2017; published online May 4, 2017. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 12(5), 051015 (May 04, 2017) (5 pages) Paper No: CND-16-1452; doi: 10.1115/1.4036519 History: Received September 25, 2016; Revised April 09, 2017

A novel synchronization scheme called special hybrid projective synchronization (SHPS), in which different state variables can synchronize up to same positive or negative scaling factors, is proposed in this paper. For all the symmetric chaotic systems, research results demonstrate that the SHPS can be realized with a single-term linear controller. Taking unified chaotic system with unknown parameter as an example, based on Lyapunov stability theory, some sufficient conditions and a parameter update law are derived for the implementation of SPHS, which are verified by some corresponding numerical simulations.

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Figures

Grahic Jump Location
Fig. 1

Time evolutions of the three corresponding states in systems (10) and (11) when α = 0

Grahic Jump Location
Fig. 2

Time evolutions of the errors between systems (10) and (11) when α = 0

Grahic Jump Location
Fig. 3

Time evolutions of the unknown parameter α1 when α = 0

Grahic Jump Location
Fig. 4

Time evolutions of the errors between systems (10) and (11) when α = 0.8

Grahic Jump Location
Fig. 5

Time evolutions of the unknown parameter α1 when α = 0.8

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