Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Djennoune, Saïd; Bettayeb, Maâmar; Al‐Saggaf, Ubaid M.

doi:10.2478/amcs-2019-0014

Cited by 16 publications

(10 citation statements)

References 66 publications

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“…where x 1 , x 2 , and x 3 are the states (10). The phase portrait of the chaotic Chen system is given in Figure 1.…”

Section: Synchronization Of Time-delay Variable-order Fractional Discrete-time Chen and Rossler Chaotic Systemsmentioning

confidence: 99%

“…where x 1 , x 2 , and x 3 are the states (10). The discrete-time Rossler chaotic system is chosen as the slave system.…”

Section: Anti-synchronization Of Variable-order Fractional Discrete-time Chen and Rossler Chaotic Systemsmentioning

confidence: 99%

“…If we consider that variable-order fractional derivatives are variables with constant values [9,10], a chaotic system as a drive system having state vector X m ∈ R n and P ∈ R nxn , with n = 3, is the master system matrix, is given by the following:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

et al. 2021

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In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchronization, we use the well-known PID (Proportional-Integral-Derivative) control theory and the Lyapunov–Krasovskii stability theory for discrete systems of a variable fractional order. We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.

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“…where x 1 , x 2 , and x 3 are the states (10). The phase portrait of the chaotic Chen system is given in Figure 1.…”

Section: Synchronization Of Time-delay Variable-order Fractional Discrete-time Chen and Rossler Chaotic Systemsmentioning

confidence: 99%

“…where x 1 , x 2 , and x 3 are the states (10). The discrete-time Rossler chaotic system is chosen as the slave system.…”

Section: Anti-synchronization Of Variable-order Fractional Discrete-time Chen and Rossler Chaotic Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

et al. 2021

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“…The synchronization of a chaotic system is essential when two chaotic systems must be synchronized. Chaotic synchronization can be categorized as identical and non-identical [19][20][21][22][23][24][25]. There are plenty of papers in the literature in which this kind of synchronization controller strategy is evinced.…”

Section: Introductionmentioning

confidence: 99%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

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In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

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“…Due to its wide applications in secure communication, synchronization of fractional-order delayed chaotic systems are extensively investigated [18][19][20][21]. However, all the above-mentioned and other synchronization schemes are in traditional drive-response ways, which only have unique drive and response systems.…”

Section: Introductionmentioning

confidence: 99%

Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems

Wang

Zhou

2019

Applied Sciences

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Multi-switching combination synchronization of three fractional-order delayed systems is investigated. This is a generalization of previous multi-switching combination synchronization of fractional-order systems by introducing time-delays. Based on the stability theory of linear fractional-order systems with multiple time-delays, we propose appropriate controllers to obtain multi-switching combination synchronization of three non-identical fractional-order delayed systems. In addition, the results of our numerical simulations show that they are in accordance with the theoretical analysis. Appl. Sci. 2019, 9, 4348 2 of 17 anti-decode and anti-attack abilities in image encryption and secure communication, in which origin messages are split into two parts and each part can be embedded into two separate drive systems. There are many works on combination synchronization [23][24][25][26]. To further strengthen the security in secure communication, Vincent et al. [27] proposed multi-switching combination synchronization scheme, in which the two drive systems are synchronized with the response system in different states. Based on the nonlinear control technique, Zheng [28] studied multi-switching combination synchronization of three non-identical chaotic systems. Khan [29] investigated adaptive multi-switching combination synchronization among three non-identical chaotic systems. In [30], Ahmad et al. proposed globally exponential multi-switching combination synchronization scheme, and applied it to secure communications. Multi-switching combination synchronization was applied in encrypted audio communication in [31]. The previous work on multi-switching combination synchronization schemes are based on integral-order chaotic systems. To improve the security in these synchronization schemes, based on fractional-order chaotic systems, Bhat et al. [32] extended the work in [27] to study multi-switching combination synchronization among three non-identical fractional-order chaotic systems. Khan et al. [33] investigated multi-switching combination-combination synchronization among a class of four non-identical fractional-order chaotic systems. In multi-switching combination-combination synchronization scheme, the state variables of two drive systems synchronize with different state variables of two response systems simultaneously, which makes the security of this scheme higher than that in [32].Since time-delay is a frequently encountered phenomenon in real applications, and the time-delay can be used as an additional parameter in synchronization to increase security in secure communication, we consider the work in [32] to investigate multi-switching combination synchronization scheme for non-identical fractional-order delayed systems by introducing time-delays in fractional-order systems.The rest of this paper is organized as follows. In Section 2, the concept of fractional calculus and the stability theory of linear fractional-order systems with multiple time-delays are briefly introduced. The multi-switching combinati...

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Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Cited by 16 publications

References 66 publications

Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems

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