Matlab Solutions of Chaotic Fractional Order Circuits

Zdzislaw, W Trzaska

doi:10.5772/23144

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…Many researches have been carried out in the last decade on fractional order systems and their applications [38][39][40]. Numerical methods to simulate fractional-order nonlinear system have been proposed in [41], and Matlab solutions for fractional-order chaotic systems have been discussed in [42]. Field Programmable Gate Array (FPGA) implementation of chaotic systems has been a hot topic recently [43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Karthikeyan¹,

Duraisamy²,

Nazarimehr³

et al. 2019

RADIOENGINEERING

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In this paper a modified third order Wien bridge oscillator with fractional order memristor is proposed. Various dynamical properties of the proposed oscillator are investigated such as equilibrium points, Eigenvalues, Lyapunov exponents and bifurcation diagrams. The Lyapunov spectrum of the system for various values of fractional order is derived. Using forward and backward continuation methods of plotting bifurcation diagram, the multistability of the oscillator is investigated. The proposed oscillator is realized using Field Programmable Gate Arrays and the experiment is conducted using hardwaresoftware co-simulation.

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Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Karthikeyan¹,

Duraisamy²,

Nazarimehr³

et al. 2019

RADIOENGINEERING

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“…The challenge while implementing the systems in FPGAs is to design the fractional order integrator which is not a readily available block in the System Generator [21,22]. Hence we implement the fractional integrators using the mathematical relation [32,33] discussed in (4), (5), and (6) and the value of ℎ is taken as 0.001 with the initial conditions as described in Table 1 and the commensurate fractional order taken as = 0.991 for FONCS-1, = 0.995 for FONCS-2, = 0.989 for FONCS-3, and = 0.99 for FONCS-4. Figures 17, 18(a), and 18(b) show the Xilinx RTL schematics of the FONCS-1 system implemented in Kintex-7 (device = 7k160t, package = fbg484 S), power utilized by the system, and power utilized for various fractional orders, respectively.…”

Section: Fpga Implementation Of the Fractional Order Novel Cubic Nonlmentioning

confidence: 99%

“…Memristor based fractional order system with a capacitor and an inductor is discussed [31]. Numerical analysis and methods for simulating fractional order nonlinear system are proposed by Petras [32] and MATLAB solutions for fractional order chaotic systems are discussed by Trzaska Zdzislaw [33]. A FPGA implementation of fractional order chaotic system using approximation method is investigated recently for the first time [21,22].…”

Section: Introductionmentioning

confidence: 99%

Hyperchaotic Chameleon: Fractional Order FPGA Implementation

2017

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There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA) implementations of the systems with their power and resource utilization are presented.

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“…Fractional order nonlinear systems with different control approaches are investigated [15][16][17]. Numerical analysis and methods for simulating fractional order nonlinear system are proposed by Petras [18] and MATLAB solutions for fractional order chaotic systems, discussed by Trzaska Zdzislaw [19]. A fractional order control based approach is proposed for piezoactuated nanopositioning stage to suppress the vibration of the low-damped resonant mode and also to minimize the tracking error for nanopositioning applications and it is proposed [20].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

Rajagopal

Karthikeyan

Duraisamy

2017

Shock and Vibration

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We investigate the chaotic oscillations in a fractional order model of a portal frame with nonideal loading. The bifurcation of the fractional order portal frame system for parameters and fractional orders are investigated. Bicoherence analysis shows the existence of quadratic nonlinearities. Fractional order adaptive sliding mode controllers are designed to suppress the chaotic oscillations with uncertain parameters. Power efficiency analysis of the FPGA implemented control scheme shows the maximum power utilization in the fractional order showing the largest Lyapunov exponent.

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Matlab Solutions of Chaotic Fractional Order Circuits

Cited by 6 publications

References 25 publications

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Hyperchaotic Chameleon: Fractional Order FPGA Implementation

Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

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