Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

He, Shaobo; Sun, Kehui; Mei, Xiaoyong; Yan, Bo; Xu, Shilong

doi:10.1140/epjp/i2017-11306-3

Cited by 92 publications

(56 citation statements)

References 20 publications

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“…The conformable derivatives may not be seen as fractional derivative but can be considered to be a natural extension of the conventional derivative. Some interesting works involving these conformable derivatives have been reported in [25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Solís-Pérez

Gómez-Aguilar

Băleanu

et al. 2018

Entropy

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This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and β-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and β-conformable attractors are provided to illustrate the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Solís-Pérez

Gómez-Aguilar

Băleanu

et al. 2018

Entropy

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“…However, to our best knowledge, there are only two literatures reporting numerical analysis of CF chaotic systems. He et al [29] firstly solved the nonlinear CF equations by the conformable Adomian decomposition method (CADM) and found chaos in the CF simplified Lorenz system. Later, Ruan et al [30] investigated dynamics of a CF memristor system based on CADM, and rich dynamical behaviors were found.…”

Section: Introductionmentioning

confidence: 99%

Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

Banerjee

2018

Complexity

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Application of conformable fractional calculus in nonlinear dynamics is a new topic, and it has received increasing interests in recent years. In this paper, numerical solution of a conformable fractional nonlinear system is obtained based on the conformable differential transform method. Dynamics of a conformable fractional memcapacitor (CFM) system is analyzed by means of bifurcation diagram and Lyapunov characteristic exponents (LCEs). Rich dynamics is found, and coexisting attractors and transient state are observed. Symbol complexity of the CFM system is estimated by employing the symbolic entropy (SybEn) algorithm, symbolic spectral entropy (SybSEn) algorithm, and symbolic C 0 (SybC 0 ) algorithm. It shows that pseudorandom sequences generated by the system have high complexity and pass the rigorous NIST test. Results demonstrate that the conformable memcapacitor nonlinear system can also be a good model for real applications.

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“…e distribution of energy in Fourier transform domain is calculated, and then the SE value is calculated by Shannon entropy, which reflects the disorder of time series in frequency domain [61,101,102]. e chaotic diagram using the complexity of SE usually reflects the spatial complexity of chaotic system parameters.…”

Section: Complexity Analysis By Spectral Entropymentioning

confidence: 99%

Analysis and FPGA Realization of a Novel 5D Hyperchaotic Four-Wing Memristive System, Active Control Synchronization, and Secure Communication Application

Liu

et al. 2019

Complexity

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By introducing a flux-controlled memristor with quadratic nonlinearity into a 4D hyperchaotic system as a feedback term, a novel 5D hyperchaotic four-wing memristive system (HFWMS) is derived in this paper. The HFWMS with multiline equilibrium and three positive Lyapunov exponents presented very complex dynamic characteristics, such as the existence of chaos, hyperchaos, limit cycles, and periods. The dynamic characteristics of the HFWMS are analyzed by using equilibria, phase portraits, poincare map, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. Of particular interest is that this novel system can generate two-wing hyperchaotic attractor under appropriate parameters and initial conditions. Moreover, the FPGA realization of the novel 5D HFWMS is reported, which prove that the system has complex dynamic behavior. Finally, synchronization of the 5D hyperchaotic system with different structures by active control and a secure signal masking application of the HFWMS are implemented based on numerical simulations and FPGA. This research demonstrates that the hardware-based design of the 5D HFWMS can be applied to various chaos-based embedded system applications including random number generation, cryptography, and secure communication.

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Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

Cited by 92 publications

References 20 publications

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

Analysis and FPGA Realization of a Novel 5D Hyperchaotic Four-Wing Memristive System, Active Control Synchronization, and Secure Communication Application

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