Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Li, Zhonghui; Xia, Tongshui; Jiang, Chen

doi:10.3390/e21050481

Cited by 8 publications

(3 citation statements)

References 40 publications

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“…In [ 39 ], dual-function projective synchronization has been achieved between fractional-order complex T system and complex Lu system. The modified projective synchronization between fractional-order complex systems has been enquired in [ 24 , 30 ] and dual-phase, dual anti-phase synchronization in fractional real variables and complex variables with uncertainties have been studied in [ 38 ].…”

Section: Introductionmentioning

confidence: 99%

The large key space image encryption algorithm based on modulus synchronization between real and complex fractional-order dynamical systems

Muthukumar¹,

Nasreen

2022

Multimed Tools Appl

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This paper constructs and analyzes the dynamical properties of a new fractional-order real hyper-chaotic system and its corresponding complex variable system. A thorough analysis was done by employing stability of equilibrium points, phase plots, Lyapunov spectrum, and bifurcation analysis for the consequences of varying fractional-order derivative and parameter values on the system. For the first time, a modulus synchronization scheme is proposed to synchronize real and complex fractional-order dynamical systems. Based on Lyapunov stability theory, non-linear controllers are designed to achieve the proposed modulus synchronization scheme. A new modulus synchronization encryption algorithm with a large key space size for digital images is introduced for the application. The experimental results and analysis validate the desired algorithm. Also, we compare our result of the new encryption algorithm with the previously published literature and verify the efficacy of the considered scheme. Numerical simulations are given to validate the theoretical analysis

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Section: Introductionmentioning

confidence: 99%

The large key space image encryption algorithm based on modulus synchronization between real and complex fractional-order dynamical systems

Muthukumar¹,

Nasreen

2022

Multimed Tools Appl

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“…Fractional calculus has unique memory properties and the ability to accurately model the system [4]. Therefore, the fractional order dynamic systems can more truly reflect the situation of the system itself and present the physical phenomena reflected by the system, so the use of fractional calculus can more accurately describe the chaotic phenomenon [5], [6].…”

Section: Introductionmentioning

confidence: 99%

Event-Triggered Adaptive Neural Network Backstepping Sliding Mode Control for Fractional Order Chaotic Systems Synchronization With Input Delay

2021

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This paper investigates the fractional order chaotic systems synchronization with input delay. To reduce the utilization of communication resources and achieve system synchronization, an adaptive neural network backstepping sliding mode controller is proposed based on event-triggered scheme without Zeno behavior. To avoid ''explosion of complexity'' and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. The sliding term is introduced to enhance robustness. The Pade delay approximation method is used to handle the input delay, which can reduce the analysis complexity of fractional order chaotic systems with input delay. The unknown nonlinear functions and uncertain disturbances are approximated by the RBF neural network. An observer is used for state estimation of the fractional order system. By applying the Lyapunov stability theory, we can prove that the all closed-loop signals are bounded. Examples and simulations prove the feasibility of the proposed control method.INDEX TERMS Fractional order chaotic systems synchronization, event-triggered, dynamic surface control, neural network, observer, input delay.

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“…e chaotic systems have much importance in modeling real-world problems in many fields: in physics [34,35], in economics and finance [1,27,36], and in electrical circuits notably [37,38]. Nowadays, there exist many investigations related to chaotic and hyperchaotic systems.…”

Section: Introductionmentioning

confidence: 99%

On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative

Sene

Ndiaye

2020

Journal of Mathematics

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In this paper, we consider a class of fractional-order systems described by the Caputo derivative. The behaviors of the dynamics of this particular class of fractional-order systems will be proposed and experienced by a numerical scheme to obtain the phase portraits. Before that, we will provide the conditions under which the considered fractional-order system’s solution exists and is unique. The fractional-order impact will be analyzed, and the advantages of the fractional-order derivatives in modeling chaotic systems will be discussed. How the parameters of the model influence the considered fractional-order system will be studied using the Lyapunov exponents. The topological changes of the systems and the detection of the chaotic and hyperchaotic behaviors at the assumed initial conditions and the considered fractional-order systems will also be investigated using the Lyapunov exponents. The investigations related to the Lyapunov exponents in the context of the fractional-order derivative will be the main novelty of this paper. The stability analysis of the model’s equilibrium points has been focused in terms of the Matignon criterion.

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Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Cited by 8 publications

References 40 publications

The large key space image encryption algorithm based on modulus synchronization between real and complex fractional-order dynamical systems

The large key space image encryption algorithm based on modulus synchronization between real and complex fractional-order dynamical systems

Event-Triggered Adaptive Neural Network Backstepping Sliding Mode Control for Fractional Order Chaotic Systems Synchronization With Input Delay

On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative

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