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Research Papers

Full State Hybrid Projective Synchronization and Parameters Identification for Uncertain Chaotic (Hyperchaotic) Complex Systems

[+] Author and Article Information
Fangfang Zhang

e-mail: zhff4u@163.com

Shutang Liu

e-mail: stliu@sdu.edu.cn
College of Control Science and Engineering,
Shandong University,
No. 17923 Jingshi Road,
Jinan 250061, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 6, 2013; final manuscript received September 4, 2013; published online October 30, 2013. Assoc. Editor: Eric A. Butcher.

J. Comput. Nonlinear Dynam 9(2), 021009 (Oct 30, 2013) (9 pages) Paper No: CND-13-1027; doi: 10.1115/1.4025475 History: Received February 06, 2013; Revised September 04, 2013

We introduce the definition of full state hybrid projective synchronization (FSHPS) with complex scaling factors for chaotic and hyperchaotic complex systems and design adaptive FSHPS schemes for uncertain chaotic complex systems under bounded disturbances with all possible situations of unknown parameters. The proposed schemes guarantee adaptive FSHPS between two chaotic complex systems with a small error bound and the convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Then we draw on the sufficient condition and necessary condition that the unknown parameters converge to their true values based on the persistency of excitation (PE) and linear independence (LI). At last, we realize adaptive FSHPS between uncertain complex Chen and Lü systems, which verify the feasibility and effectiveness of the presented schemes.

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Figures

Grahic Jump Location
Fig. 1

The FSHPS between Eqs. (40) and (41) with η1 = η21 = η2 = η3 = 10, τ1 = τ2 = τ3 = 10, γ1 = γ2 = γ3 = 10, and the complex scaling factors 1+j,2-j,-1

Grahic Jump Location
Fig. 2

The error dynamic of the FSHPS between Eqs. (40) and (41) with η1 = η21 = η2 = η3 = 10, τ1 = τ2 = τ3 = 10, γ1 = γ2 = γ3 = 10, and the complex scaling factors 1+j,2-j,-1. Here, e1 = x1r-(h1z1r-h2z1i) = x1r-(z1r-z1i), e2 = x1i-(h2z1r+h1z1i) = x1r-(z1r+z1i), e3 = x2r-(2z2r+z2i), e4 = x2i-(-z2r+2z2i), and e5 = x3+z3.

Grahic Jump Location
Fig. 3

The identification process of the unknown parameter vector A with η1 = η21 = η2 = η3 = 10, τ1 = τ2 = τ3 = 10, γ1 = γ2 = γ3 = 10, and the complex scaling factors 1+j,2-j,-1

Grahic Jump Location
Fig. 4

The identification process of the unknown parameter vector B with η1 = η21 = η2 = η3 = 10, τ1 = τ2 = τ3 = 10, γ1 = γ2 = γ3 = 10, and the complex scaling factors 1+j,2-j,-1

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