FPGA implementation of fractional-order chaotic systems

Shah, Divya K.; Chaurasiya, Rohit B.; Vyawahare, Vishwesh A.; Pichhode, Khushboo; Patil, Mukesh D.

doi:10.1016/j.aeue.2017.05.005

Cited by 60 publications

(15 citation statements)

References 24 publications

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“…In this section, the nonlinear behavior of the two saturable inductor resonant circuit is investigated. Those systems have been discussed in [40,54].Various dynamical properties of them are derived in this part. Figure 1 shows the two saturable reactor circuit with two resistors, a capacitor, a periodic exciter, a DC potential and two saturable inductors.…”

Section: Saturable Reactor Circuit (Src)mentioning

confidence: 99%

“…In addition, the saturated inductors reduce the size of the overall circuit compared to the non-saturated inductors [41]. A resonant circuit with two saturated inductors [40] and the existence of quasi-periodic invariable tori has been discussed in [44]. Bifurcation analysis of the two saturated inductor resonant circuit has been discussed with a three dimensional Duffing type equation in [54] considering the system as a non-autonomous type.…”

Section: Introductionmentioning

confidence: 99%

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Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

Rajagopal

Jafari

Kaçar

et al. 2019

ITC

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Chaos is often observed in forced nonlinear electrical circuits with saturable reactors. Simplest of such a circuit is presented and investigated in both integer order and non-integer (fractional) order form. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used. Some dynamic properties of the novel system are investigated. For implementing the system in field programmable gate arrays (FPGA), the Adomian decomposition method is used. Power and resource utilization of the fractional order system for implementing in FPGA are presented. Also, in this work, a novel fractional based sound encryption application is implemented as a unique application.

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Section: Saturable Reactor Circuit (Src)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

Rajagopal

Jafari

Kaçar

et al. 2019

ITC

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“…In addition, the experimental verification of fractional-order models is a topic that has been attracting the attention of researchers [35][36][37][38][39]. In this scenario, ARM-based embedded systems have become in a central block integrated with non-embedded technologies, such as FPGAs, DSPs, and microcontrollers.…”

Section: Introductionmentioning

confidence: 99%

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

2020

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For studying biological conditions with higher precision, the memory characteristics defined by the fractional-order versions of living dynamical systems have been pointed out as a meaningful approach. Therefore, we analyze the dynamics of a glucose-insulin regulatory system by applying a non-local fractional operator in order to represent the memory of the underlying system, and whose state-variables define the population densities of insulin, glucose, and β-cells, respectively. We focus mainly on four parameters that are associated with different disorders (type 1 and type 2 diabetes mellitus, hypoglycemia, and hyperinsulinemia) to determine their observation ranges as a relation to the fractional-order. Like many preceding works in biosystems, the resulting analysis showed chaotic behaviors related to the fractional-order and system parameters. Subsequently, we propose an active control scheme for forcing the chaotic regime (an illness) to follow a periodic oscillatory state, i.e., a disorder-free equilibrium. Finally, we also present the electronic realization of the fractional glucose-insulin regulatory model to prove the conceptual findings.

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“…FPGA is also used in fast prototyping for Application Specific Integrated Circuit (ASIC) [56]- [58]. Some FPGA implementations use software tools to generate the Register Transfer Level (RTL) as LABVIEW and MATLAB Simulink [59], [60]. A new algorithm for the implementation of GL operators based on the linear approximation approach was introduced in [61].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics and FPGA Implementation of a Fractional-Order Chaotic System With Time Delay

Sayed

Roshdy

Said

et al. 2020

IEEE Open J. Circuits Syst.

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This article proposes a numerical solution approach and Field Programmable Gate Array implementation of a delayed fractional-order system. The proposed method is amenable to a sufficiently efficient hardware realization. The system's numerical solution and hardware realization have two requirements. First, the delay terms are implemented by employing LookUp Tables to keep the already required delayed samples in the dynamical equations. Second, the fractional derivative is numerically approximated using Grünwald-Letnikov approximation with a memory window size, L, according to the short memory principle such that it balances between accuracy and efficiency. Bifurcation diagrams and spectral entropy validate the chaotic behaviour of the system for commensurate and incommensurate orders. Additionally, the dynamic behaviour of the system is studied versus the delay parameter, τ , and the window size, L. The system is realized on Nexys 4 Artix-7 FPGA XC7A100T with throughput 1.2 Gbit/s and hardware resources utilization 15% from the total LookUp Tables and 4% from the slice registers. Oscilloscope experimental results verify the numerical solution of the delayed fractional-order system. The amenability to digital hardware realization, which is experimentally validated in this article, is added to the system's advantages and encourages its utilization in future digital applications such as chaos control and synchronization and chaos-based communication applications.INDEX TERMS Chaos, fractional-order systems, FPGA, time-delay.

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FPGA implementation of fractional-order chaotic systems

Cited by 60 publications

References 24 publications

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

Chaotic Dynamics and FPGA Implementation of a Fractional-Order Chaotic System With Time Delay

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