The Shortest Synchronization Time with Optimal Fractional Order Value Using a Novel Chaotic Attractor Based on Secure Communication

Durdu, Ali̇; Uyaroğlu, Yılmaz

doi:10.1016/j.chaos.2017.08.008

Cited by 21 publications

(6 citation statements)

References 22 publications

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“…5 is the diagram of error states. It demonstrates that the error system (25) tends to zero and two different Lorenz systems obtain MPFS with the controller (26). Note that the parameters of k 1 , k 2 are larger than k 3 due to the complexity of scaling functions h 1 (t), h 2 (t).…”

Section: F Function Projective Synchronizationmentioning

confidence: 92%

N-Systems Function Projective Combination Synchronization—A Review of Real and Complex Continuous Time Chaos Synchronization

et al. 2019

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As an important branch in the field of chaos, chaos synchronization (CHS) has attracted great attentions since it was firstly proposed. In this review article, numerous types of continuous time CHS are presented for the past 29 years. Previous CHS are divided into two major parts: one is CHS in real number field, and the other is CHS in complex number field. Some classic types of CHS, controllers and corresponding stability theories are preliminarily reviewed. Besides, a new type of chaos synchronization is proposed, which is called N-systems combination function projective synchronization (NCOFPS). Interestingly and importantly, most of these proposed types of CHS belong to NCOFPS. Then, time delay function projective synchronization (TDFPS) is also proposed, which is one of the types of NCOFPS and never studied in existed papers. And TDFPS controller, corresponding mathematical proof are obtained and simulation experiments illustrate the effectiveness of investigated controller. This paper provides a generalized view to catch the development of CHS in different fields. Finally, we give the conclusions and prospects of CHS.

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Section: F Function Projective Synchronizationmentioning

confidence: 92%

N-Systems Function Projective Combination Synchronization—A Review of Real and Complex Continuous Time Chaos Synchronization

et al. 2019

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“…In this paper, the corresponding cross-section X = |MNPQ| firstly was choosed on the plane (7), which is show in Fig 5 with its four vertices M = [0, 1,1], N = [0, 0, 9], P = [0, 4,9], Q = [0, 4,1] and then define the poincaré map ω : R → Γ as follows: for each point x ∈ R=|ABCD|, ω(x) is the first return intersection point with |ABCD| under the flow of system (1) with initial condition x = (0, y, z). Through a lot of attempts, we finally choose a subset R = |ABCD| in X, with four vertices A = [0, 0.5402, 3.855], B = [0, 0.7666, 3.599], C = [0, 1.253, 4.322], D = [0, 0.899, 4.353].…”

Section: Horseshoe In the Fractional-order Liu Systemmentioning

confidence: 99%

“…It has been found that fractional calculus provides a realistic description of some physical natural phenomena [1,2]. Fractional calculus has been also successfully applied in the fields of signal processing, economics, mechanical engineering and secure communications [3][4][5][6][7]. Fractional-order systems (FOS) can describe the inherent characteristics and physical properties more accurately [8].…”

Section: Introductionmentioning

confidence: 99%

Topological Horseshoe Analysis and FPGA Implementation of the Fractional-order Liu System

E¹,

Yuan²,

Tong³

et al. 2018

Preprint

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This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

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“…It has been found that fractional calculus provide a realistic description of some physical natural phenomena [1], [2]. Fractional calculus has been also successfully applied in the fields of signal processing, economics, mechanical engineering and secure communications [3]- [6]. Fractional-order systems (FOS) can describe the inherent characteristics and physical properties more accurately [7].…”

Section: Introductionmentioning

confidence: 99%

Topological Horseshoe Analysis and FPGA Implementation of a Classical Fractional Order Chaotic System

et al. 2019

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Scholars have done extensive research on dynamic analysis and analog circuits implementation of the classical fractional order chaotic system-Liu System (FOLS). However, they did not rigorously prove the existence of FOLS from the perspective of mathematics. And they also did not effectively design digital circuits to generate signals of the fractional order chaotic systems, especially the 2.7-order system. This paper selects an appropriate Poincaré section where a first return Poincaré map of FOLS was defined. Based on computer-assisted verification method, the conclusion is that the Poincaré map is semi-conjugate to a 2-shift map and the topological entropy of the map is no less than ln 2, which rigorously verifies the existence of chaotic behavior in the 2.7-order Liu system. This proof is necessary before the chaotic system is used for information encryption. The next and most significant task is to build a system model through DSP-Builder software and generate chaotic signals using Field Programmable Gate Array chip. The results of oscilloscope consistent with numerical simulations, which lays the foundation for image and video streaming encryption.INDEX TERMS Computer-assisted proof, fractional order liu System, FPGA implementation, topological horseshoe analysis.

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The Shortest Synchronization Time with Optimal Fractional Order Value Using a Novel Chaotic Attractor Based on Secure Communication

Cited by 21 publications

References 22 publications

N-Systems Function Projective Combination Synchronization—A Review of Real and Complex Continuous Time Chaos Synchronization

N-Systems Function Projective Combination Synchronization—A Review of Real and Complex Continuous Time Chaos Synchronization

Topological Horseshoe Analysis and FPGA Implementation of the Fractional-order Liu System

Topological Horseshoe Analysis and FPGA Implementation of a Classical Fractional Order Chaotic System

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