Fractional analysis of co-existence of some types of chaos synchronization

Ouannas, Adel; Odibat, Zaid; Hayat, Tasawar

doi:10.1016/j.chaos.2017.10.031

Cited by 27 publications

(9 citation statements)

References 36 publications

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“…Solution. Applying the inverse operator of C 0 D to the system Equations (28), (29), (30) and considering the initial conditions given by Equation (31), we get…”

Section: Examplementioning

confidence: 99%

“…where X(t) is the vector of states in x, y, and z. Then, an exact solution of Equations (28)- (30) in the form of the expression (36) allows a comparison with the -expansion…”

Section: Examplementioning

confidence: 99%

“…27,28 Chaos theory is a branch of mathematics with several applications in physics, engineering, economics, and biology. [29][30][31][32] In the work of Li et al, 33 the master-slave synchronization of fractional-order chaotic systems via Riemann-Liouville derivative was studied, two examples were treated, ie, Chua's and Rössler's attractors. In the work of Mahmoud et al, 34 the authors investigated the control of chaotic Burke-Shaw system using the Pyragas method.…”

Section: Introductionmentioning

confidence: 99%

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Fractional conformable attractors with low fractality

Morales‐Delgado

Gómez‐Aguilar

Escobar-Jiménez

2018

Math Methods in App Sciences

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In this paper, we considered a fractional conformable derivative of Liouville-Caputo type of fractional-order = n − , which contains a small perturbation and positive integer n values between [0;1] to obtain the solutions of three different fractional conformable attractors (Chen's attractor, Genesio-Tesi's attractor, and Liu's attractor). The fractional conformable Adomian decomposition method is applied to obtain an expansion of the fractional conformable derivative in = n − . The solutions of the fractional chaotic systems are calculated in the form of convergent series. We investigate the dynamics of these attractors by numerical simulations for different fractional orders values and parameter . KEYWORDSadomian decomposition method, chaos, fractional calculus, fractional conformable derivative, low-fractality 6378

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“…Solution. Applying the inverse operator of C 0 D to the system Equations (28), (29), (30) and considering the initial conditions given by Equation (31), we get…”

Section: Examplementioning

confidence: 99%

“…where X(t) is the vector of states in x, y, and z. Then, an exact solution of Equations (28)- (30) in the form of the expression (36) allows a comparison with the -expansion…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional conformable attractors with low fractality

Morales‐Delgado

Gómez‐Aguilar

Escobar-Jiménez

2018

Math Methods in App Sciences

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“…Various kinds of control schemes have been introduced in the past to synchronize dynamical systems such as complete (anti-) synchronization [3], lag synchronization [4], function projective synchronization [5], generalized synchronization [6], and Q-S synchronization [7]. Recently, the topic of synchronization between dynamical systems described by fractional-order differential equations started to attract increasing attention [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Synchronization results for a class of fractional-order spatiotemporal partial differential systems based on fractional Lyapunov approach

et al. 2019

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In this paper, the problem of synchronization of a class of spatiotemporal fractional-order partial differential systems is studied. Subject to homogeneous Neumann boundary conditions and using fractional Lyapunov approach, nonlinear and linear control schemes have been proposed to synchronize coupled general fractional reaction-diffusion systems. As a numerical application, we investigate complete synchronization behaviors of coupled fractional Lengyel-Epstein systems.

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“…This phenomenon is commonly referred to as the co-existence of synchronization types. Many studies can be found in the literature proposing linear and nonlinear control laws that give rise to the co-existence phenomenon for continuous-time integer-order systems [33], continuous-time fractional systems [34][35][36][37][38], and discrete-time integer-order systems [39][40][41]. However, to the best of the authors' knowledge, no such studies have been made for fractional-order discrete-time systems.…”

Section: Introductionmentioning

confidence: 99%

The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders

Bendoukha

Ouannas

Wang

et al. 2018

Entropy

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This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings.

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Fractional analysis of co-existence of some types of chaos synchronization

Cited by 27 publications

References 36 publications

Fractional conformable attractors with low fractality

Fractional conformable attractors with low fractality

Synchronization results for a class of fractional-order spatiotemporal partial differential systems based on fractional Lyapunov approach

The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders

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