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Research Papers

Adaptive Hybrid Function Projective Synchronization of General Chaotic Complex Systems With Different Orders

[+] Author and Article Information
Ping Liu

College of Mechanical and
Electronic Engineering,
Shandong Key Laboratory of
Gardening Machinery and Equipment,
Shandong Agricultural University,
Taian 271018, China
e-mail: liupingshd@126.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 25, 2014; final manuscript received July 3, 2014; published online January 12, 2015. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 10(2), 021018 (Mar 01, 2015) (10 pages) Paper No: CND-14-1029; doi: 10.1115/1.4027975 History: Received January 25, 2014; Revised July 03, 2014; Online January 12, 2015

A lot of progress has been made in the research of hybrid function projective synchronization (HFPS) for chaotic real nonlinear systems, while the HFPS of two different chaotic complex nonlinear systems with nonidentical dimensions is seldom reported in the literatures. So this paper discusses the HFPS of general chaotic complex system described by a unified mathematical expression with different dimensions and fully unknown parameters. Based on the Lyapunov stability theory, the adaptive controller is designed to synchronize two general uncertain chaotic complex systems with different orders in the sense of HFPS and the parameter update laws for estimating unknown parameters of chaotic complex systems are also given. Moreover, the control coefficients can be automatically adapted to updated laws. Finally, the HFPS between hyperchaotic complex Lorenz system and complex Chen system and that between chaotic complex Lorenz system and hyperchaotic complex Lü are taken as two examples to demonstrate the effectiveness and feasibility of the proposed HFPS scheme.

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References

Figures

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Fig. 5

The graph of the errors between the projection z1z2z4 of the hyperchaotic complex Lorenz system and chaotic complex Chen system

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Fig. 6

Changing parameters a∧1,a∧3, and a∧4 with time t

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Fig. 7

Changing parameters b∧1,b∧2, and b∧3 with time t

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Fig. 8

Time evolution of control coefficients k1, k2, and k3

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Fig. 9

The errors between the added-order complex Lorenz system and the hyperchaotic complex Lü system

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Fig. 10

Changing parameters a∧1,a∧2, and a∧3 with time t

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Fig. 11

Changing parameters b∧1,b∧2,b∧3, and b∧4 with time t

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Fig. 12

Time evolution of control coefficients k1, k2, k3, and k4

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Fig. 14

Changing parameters a∧1,a∧2, and a∧3 with time t

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Fig. 15

Changing parameters b∧1,b∧2,b∧3, and b∧4 with time t

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Fig. 16

Time evolution of control coefficients k1, k2, k3, and k4

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Fig. 4

Time evolution of control coefficients k1, k2, and k3

Grahic Jump Location
Fig. 3

Changing parameters b∧1,b∧2, and b∧3 with time t

Grahic Jump Location
Fig. 2

Changing parameters a∧1,a∧2, and a∧3 with time t

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Fig. 1

The graph of the errors between the projection z1z2z3 of the hyperchaotic complex Lorenz system and chaotic complex Chen system

Grahic Jump Location
Fig. 13

The graph of the errors between the added-order complex Lorenz system and the hyperchaotic chaotic complex Lü system

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