Topological horseshoe analysis on a four-wing chaotic attractor and its FPGA implement

Dong, Enzeng; Liang, Zhihan; Du, Shengzhi; Chen, Zengqiang

doi:10.1007/s11071-015-2352-2

Cited by 55 publications

(15 citation statements)

References 40 publications

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“…Implementation of chaotic and hyperchaotic systems using Field Programmable Gate Arrays (FPGA) has been widely investigated [41][42][43]. Chaotic random number generators have been implemented in FPGA for applications in image cryptography [44].…”

Section: Fpga Implementationmentioning

confidence: 99%

A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus

et al. 2018

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Although many mathematical models have been presented for glucose and insulin interaction, none of these models can describe diabetes disease completely. In this work, the dynamical behavior of a regulatory system of glucose-insulin incorporating time delay is studied and a new property of the presented model is revealed. This property can describe the diabetes disease better and therefore may help us in deeper understanding of diabetes, interactions between glucose and insulin, and possible cures for this widespread disease.

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Section: Fpga Implementationmentioning

confidence: 99%

A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus

et al. 2018

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“…A set having the three properties in the above proposition is often defined as a Cantor set, such a Cantor set frequently appears in characterization of complex structure of invariant set in a chaotic dynamical system [8,20,25].…”

Section: Preliminarymentioning

confidence: 99%

“…Furthermore, the topological horseshoe lemma was proposed as a practical and useful computer-assisted proof method [16]. This theory has already been used to prove the existence of chaos in some integer-order systems, for example Dong et al proved its existence in typical 3D systems [17][18][19][20], Wang et al proved the chaos existence in hyperchaos system [21][22][23][24], Jia et al analyzed the existence of chaos in fractional order Lü chaotic systems [25][26][27][28].…”

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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“…Recently many digital implementations of chaotic systems have been proposed and implemented in field programmable gate arrays (FPGA) [29][30][31]. Image crypto systems using chaotic random number generators are implemented in FPGA and are of greater interest because of the robustness and complexity of the chaos encryption systems [32].…”

Section: Introductionmentioning

confidence: 99%

Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation

Karthikeyan

Rajagopal

2017

Complexity

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We investigate a specific smart grid system and its nonlinear properties. Lyapunov exponents are derived to prove the existence of chaos and bifurcation and bicoherence contours are investigated to show the parameter dependence and existence of quadratic nonlinearities, respectively. A fractional order model of the smart grid system (FOSG) is then derived and bifurcation of the FOSG system with variation in the commensurate fractional order of the system is investigated to show that largest Lyapunov exponent of the system exists in fractional order. Hence we proposed two different control methods to suppress the chaotic oscillations. In the first method we derive fractional order adaptive sliding mode control (FOASMC) algorithm to control chaotic oscillations and in the second method we used genetically optimized fractional order PID controllers (GAFOPID) for chaos control. Numerical simulations are conducted to show the effectiveness of the controllers and also to prove that GAFOPID controllers are more effective than FOASMC controllers for fractional order systems. The GAFOPID controllers are then realized in FPGA to show that the proposed methodology is hardware realizable.

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Topological horseshoe analysis on a four-wing chaotic attractor and its FPGA implement

Cited by 55 publications

References 40 publications

A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus

A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus

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

Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation

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