Generalized function projective synchronization via nonlinear controller strategy

Al-Azzawi, Saad Fawzi; Al-Talib, Zaidoon Sh.

doi:10.1080/09720502.2021.2008625

Cited by 8 publications

(5 citation statements)

References 24 publications

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“…then the two chaotic systems in system (1) are said to be GFPS with respect to the scaling function matrix h [37,40]. The two chaotic systems are said to be FPS if…”

Section: Gfps Scheme Between Two Different Uncertain Chaotic Systemsmentioning

confidence: 99%

“…The true values of the uncertain parameters of systems ( 38) and ( 39) are chosen as σ = 10, r = 28, β = 8/3 and a = 35, b = 3, c = 28. According to the previous analysis results in the section, if k, γ 11 , γ 21 , γ 12 , γ 22 are chosen as k = γ 11 = γ 21 = −1 and γ 12 = γ 22 = 0.01, GFPS between uncertain Lorenz and Chen chaotic systems will be achieved under the control of the controller (40), and the uncertain parameters will be estimated using the parameter update laws (41) and (42). The initial conditions are given by x 1 (0) = 0.1, x 2 (0) = 0.2, x 3 (0) = 0.3, y 1 (0) = 0.4, y 2 (0) = 0.5, y 3 (0) = 0.6, σ = 9, r = 25, β = 3, â = 33, b = 2 and ĉ = 29 to perform the numerical simulations.…”

Section: The Design Of Simple Parameter Update Lawsmentioning

confidence: 99%

“…Du et al [35] and Srisuntorn et al [36] discussed modified function projective synchronization (MFPS), in which two chaotic systems can be synchronized up to a desired scaling function matrix. As another extension of MPS and FPS, in generalized function projective synchronization (GFPS), the scaling function matrix is more generalized than that of MFPS, as has been discussed by Yu and Li [37], Li and Zhao [38], Wu et al [39] and Al-Azzawi [40].…”

Section: Introductionmentioning

confidence: 99%

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Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Zhen

2023

Applied Sciences

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This study proposes a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. The GFPS condition is derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations on the basis of the Laplace transform method and convolution theorem, which are solved by applying the successive approximation method in the theory of integral equations. Compared with the results obtained by constructing Lyapunov functions or calculating the conditional Lyapunov exponents, the uncertain parameters and the scaling function factors considered in this paper have fewer restrictions, and the parameter update laws designed for the estimation of the uncertain parameters are simpler and easier to realize physically.

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“…then the two chaotic systems in system (1) are said to be GFPS with respect to the scaling function matrix h [37,40]. The two chaotic systems are said to be FPS if…”

Section: Gfps Scheme Between Two Different Uncertain Chaotic Systemsmentioning

confidence: 99%

Section: The Design Of Simple Parameter Update Lawsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Zhen

2023

Applied Sciences

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“…It was firstly reported in 1999 when Mainieri and Rehacek studied the synchronization problem of Lorenz chaotic system. Further more, many scholars have achieved many important results, see [11][12][13][14][15] and the references therein. The definition of projective synchronization is introduced in the next.…”

Section: Introductionmentioning

confidence: 99%

Projective synchronization of the generalized Lotka-Volterra system with asymptotically unbounded external disturbance

Guo

Liu

2023

Phys. Scr.

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This paper investigates the projective synchronization problem of the generalized Lotka-Volterra (GLV) system in the presence of unbounded external disturbance. Firstly, a uniﬁed projective synchronization control law is proposed for the nominal GLV system, which veriﬁed the existence of the projective synchronization problem. Secondly, a suitable ﬁlter is designed to estimate the asymptotically unbounded external disturbance that is incorporated into GLV system, by which a simple yet general disturbance estimator-based control strategy is derived to achieve the asymptotically stable of the error system. Finally, numerical simulations are performed to demonstrate the correctness and validity of the theoretical results.

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“…Where chaos is divided into two parts: deterministic and non-deterministic chaotic systems. The first description of a chaotic process was given in 1963 by Lorenz [15] who developed a system called the Lorenz attractor, along with nonlinear differential equations [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Use Two Kind Hybridization of the Chaotic Peafowl Algorithm with the Hummingbird Algorithm

Alhamdany,

Mitras

2022

J. Al-Qadisiyah Comp. Sci. Math.

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The wide spread of living organisms in nature and how they obtain food has prompted many scientists to form mathematical models that simulate these organisms. These models were used to solve math problems that take a long time and effort to solve, but these models were sometimes weak and required modification. In this research we used two methods to reach the optimal solution, the first method we used the Peafowl optimization algorithm (POA) with the chaos function and the chaotic tent function to reach the optimal solution and this was the first step in the work, the second method we hybridized the first step by adding the artificial hummingbird algorithm (AHA) The hybridization was of two types, the first by linking communities and the second by linking equations, and we got the optimal solution using 1000 iterations in the two steps, which resulted in producing the optimal solution.

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Generalized function projective synchronization via nonlinear controller strategy

Cited by 8 publications

References 24 publications

Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Projective synchronization of the generalized Lotka-Volterra system with asymptotically unbounded external disturbance

Use Two Kind Hybridization of the Chaotic Peafowl Algorithm with the Hummingbird Algorithm

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