Dynamic analysis of seven-dimensional fractional-order chaotic system and its application in encrypted communication

Peng, Z.-S.; Yu, Wenxin; Wang, Junnian; Jing, Wang; Chen, Yu; He, Xianke; Jiang, Dan

doi:10.1007/s12652-020-01896-1

Cited by 25 publications

(8 citation statements)

References 45 publications

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“…Further papers on the neural network method were carried [41,42]. Some works on rogue waves and dynamical fluid equations were presented [43][44][45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Abdel‐Gawad

2022

Nonlinear Dyn

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A Generalized (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation (2D- gCDGKSE) is an integro-differential equation that describes tow-layer fluid interaction. The non-autonomous (2+1)-dimensional gCDGKSE (NAUT-gCDGKSE) was rarely considered in the literature. In the previous works, the concepts of two-layer fluid interaction and non-uniform fluid were not explored. This motivated us to focus the attention on these themes. Our objective is to inspecting waves structures in non-uniform fluid which describes fluid flows near a solid boundary. Thus, the present work is completely new. Our objective, here, is to inspect waves which are similar to those created in waterfall, water waves behind dams, boat sailing, in the network of canals during water release, and internal waves in submarine. In a uniform fluid, rogue waves occur in open oceans and seas, while in the present case of non-uniform fluid, towering and internal rogue waves occur near barriers (islands) and near submarine, respectively. This was consolidated experimentally, as it was shown that rogue wave is produced in a water tank (which is with solid boundary). The exact solutions of NAUT-gCDGKSE are derived here, by implementing the extended unified method (EUM). In applications, it is found that the EUM is of lower time cost in symbolic computation, than when using Lie symmetry, Darboux and AutoBucklund transformations. The results obtained here are evaluated numerically, and they are displayed in graphs. They reveal multiple waves structures with relevance to waves created near a solid boundary. Among them are towering and internal rogue waves, internal (hollowed) and bulge-U-shape wave and S-shape wave, water fall, saddle wave, and dromoions.

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“…Further papers on the neural network method were carried [41,42]. Some works on rogue waves and dynamical fluid equations were presented [43][44][45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Abdel‐Gawad

2022

Nonlinear Dyn

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“…Fractionality is a branch of mathematics that is an extension of classical calculus. The study of fractional calculus has recently received a lot of attention due to its potential application in different fields [19]. In 1694, Leibniz was asked by L'Hospital if the half order derivative is possible [20].…”

Section: Introductionmentioning

confidence: 99%

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

et al. 2021

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This article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the suggested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications.

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“…Fractional-order derivatives are characterized by their memory properties providing an excellent approach for describing the physical phenomena elegantly with improved accuracy [1,2]. As a result, the researchers have proposed novel mathematical models with applications in various fields, such as biology, economics, chaos theory, botany, hidden dynamics, digital circuits, cryptography, control, image processing, wind turbines, viscoelastic studies, and ferroelectric materials [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Active Realization of Fractional‐Order Integrators and Their Application in Multiscroll Chaotic Systems

et al. 2021

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This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lü chaotic system. We base them on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions. The integrators are first-order active realizations tuned to reduce the inaccuracy of the frequency response. By an exponential curve fitting, we got a convenient design equation for realizing fractional-order integrators of orders from 0.1 to 0.95. The results include simulations in SPICE of the mathematical description and the electronic implementation and experimental measurements that confirm them. Monte Carlo and sensitivity tests revealed a robust realization. Contrary to its passive counterparts, the suggested realizations significantly reduce design and implementation efforts by favoring resistors and capacitors with commercial values and reducing hardware requirements.

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Dynamic analysis of seven-dimensional fractional-order chaotic system and its application in encrypted communication

Cited by 25 publications

References 45 publications

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

Active Realization of Fractional‐Order Integrators and Their Application in Multiscroll Chaotic Systems

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