Research Papers

Synchronization of Quadratic Chaotic Systems Based on Simultaneous Estimation of Nonlinear Dynamics

[+] Author and Article Information
Amin Zarei

Faculty of Electrical and Computer Engineering,
University of Sistan and Baluchestan,
Zahedan 9816745845, Iran
e-mail: aminzarei6429@gmail.com

Saeed Tavakoli

Faculty of Electrical and Computer Engineering,
University of Sistan and Baluchestan,
Zahedan 9816745845, Iran
e-mail: tavakoli@ece.usb.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 2, 2017; final manuscript received May 22, 2018; published online June 18, 2018. Assoc. Editor: Anindya Chatterjee.

J. Comput. Nonlinear Dynam 13(8), 081001 (Jun 18, 2018) (7 pages) Paper No: CND-17-1538; doi: 10.1115/1.4040459 History: Received December 02, 2017; Revised May 22, 2018

To synchronize quadratic chaotic systems, a synchronization scheme based on simultaneous estimation of nonlinear dynamics (SEND) is presented in this paper. To estimate quadratic terms, a compensator including Jacobian matrices in the proposed master–slave schematic is considered. According to the proposed control law and Lyapunov theorem, the asymptotic convergence of synchronization error to zero is proved. To identify unknown parameters, an adaptive mechanism is also used. Finally, a number of numerical simulations are provided for the Lorenz system and a memristor-based chaotic system to verify the proposed method.

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Grahic Jump Location
Fig. 1

Synchronization of state variables in example 1

Grahic Jump Location
Fig. 2

Synchronization error of state variables in example 1

Grahic Jump Location
Fig. 3

Input signals in example 1

Grahic Jump Location
Fig. 4

Estimation of matrix θ̂(t) in example 1

Grahic Jump Location
Fig. 5

Synchronization of state variables in example 2

Grahic Jump Location
Fig. 6

Synchronization error of state variables in example 2

Grahic Jump Location
Fig. 7

Input signals in example 2

Grahic Jump Location
Fig. 8

Estimation of matrix θ̂(t) in example 2



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