A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

In this article, the fractional calculus is introduced into a simplest memristive circuit to construct a new four-dimensional fractional-order chaotic system. Combining conformable differential definition and Adomian decomposition method (ADM) algorithm is used to solve the numerical solution of the...

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Published inIEEE access Vol. 8; pp. 199852 - 199863
Main Authors Liu, Tianming, Yu, Jiawu, Yan, Huizhen, Mou, Jun
Format Journal Article
LanguageEnglish
Published Piscataway IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Bifurcation
Bifurcations
CADM algorithm
Chaos theory
chaotic degradation
Circuits
coexistence of infinite attractors
Complexity theory
DSP implement
Dynamic characteristics
Fractional calculus
Fractional-order chaotic system
Frequency control
Liapunov exponents
Numerical stability
Phase diagrams
Simulation
Stability analysis
System performance
Online AccessGet full text
ISSN2169-3536
2169-3536
DOI10.1109/ACCESS.2020.3035368

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Abstract In this article, the fractional calculus is introduced into a simplest memristive circuit to construct a new four-dimensional fractional-order chaotic system. Combining conformable differential definition and Adomian decomposition method (ADM) algorithm is used to solve the numerical solution of the system. The attractor coexistence of the fractional-order system is investigated from the attractor phase diagram, coexistence bifurcation model, coexistence Lyapunov exponent spectrum and attractor basin. In addition, the hardware circuit of the system is implemented on the DSP platform. The simulation results show that the fractional-order chaotic system exhibits rich dynamic characteristics. In particular, the initial value of the system could control the offset, amplitude and frequency of the attractor better, and increase the complexity and randomness of the chaotic sequences. The research provides theoretical basis and guidance for the applications of fractional-order chaotic system.
AbstractList In this article, the fractional calculus is introduced into a simplest memristive circuit to construct a new four-dimensional fractional-order chaotic system. Combining conformable differential definition and Adomian decomposition method (ADM) algorithm is used to solve the numerical solution of the system. The attractor coexistence of the fractional-order system is investigated from the attractor phase diagram, coexistence bifurcation model, coexistence Lyapunov exponent spectrum and attractor basin. In addition, the hardware circuit of the system is implemented on the DSP platform. The simulation results show that the fractional-order chaotic system exhibits rich dynamic characteristics. In particular, the initial value of the system could control the offset, amplitude and frequency of the attractor better, and increase the complexity and randomness of the chaotic sequences. The research provides theoretical basis and guidance for the applications of fractional-order chaotic system.
Author Yan, Huizhen
Mou, Jun
Yu, Jiawu
Liu, Tianming
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SubjectTerms Algorithms
Bifurcation
Bifurcations
CADM algorithm
Chaos theory
chaotic degradation
Circuits
coexistence of infinite attractors
Complexity theory
DSP implement
Dynamic characteristics
Fractional calculus
Fractional-order chaotic system
Frequency control
Liapunov exponents
Numerical stability
Phase diagrams
Simulation
Stability analysis
System performance
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Title A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation
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