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    Nonlinear Dynamic Analysis of a Simplest Fractional-Order Delayed Memristive Chaotic System

    Source: Journal of Computational and Nonlinear Dynamics:;2017:;volume( 012 ):;issue: 004::page 41003
    Author:
    Hu, Wei
    ,
    Ding, Dawei
    ,
    Wang, Nian
    DOI: 10.1115/1.4035412
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: A simplest fractional-order delayed memristive chaotic system is investigated in order to analyze the nonlinear dynamics of the system. The stability and bifurcation behaviors of this system are initially investigated, where time delay is selected as the bifurcation parameter. Some explicit conditions for describing the stability interval and the transversality condition of the emergence for Hopf bifurcation are derived. The period doubling route to chaos behaviors of such a system is discussed by using a bifurcation diagram, a phase diagram, a time-domain diagram, and the largest Lyapunov exponents (LLEs) diagram. Specifically, we study the influence of time delay on the chaotic behavior, and find that when time delay increases, the transitions from one cycle to two cycles, two cycles to four cycles, and four cycles to chaos are observed in this system model. Corresponding critical values of time delay are determined, showing the lowest orders for chaos in the fractional-order delayed memristive system. Finally, numerical simulations are provided to verify the correctness of theoretical analysis using the modified Adams–Bashforth–Moulton method.
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      Nonlinear Dynamic Analysis of a Simplest Fractional-Order Delayed Memristive Chaotic System

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4236406
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    contributor authorHu, Wei
    contributor authorDing, Dawei
    contributor authorWang, Nian
    date accessioned2017-11-25T07:20:22Z
    date available2017-11-25T07:20:22Z
    date copyright2017/19/1
    date issued2017
    identifier issn1555-1415
    identifier othercnd_012_04_041003.pdf
    identifier urihttp://138.201.223.254:8080/yetl1/handle/yetl/4236406
    description abstractA simplest fractional-order delayed memristive chaotic system is investigated in order to analyze the nonlinear dynamics of the system. The stability and bifurcation behaviors of this system are initially investigated, where time delay is selected as the bifurcation parameter. Some explicit conditions for describing the stability interval and the transversality condition of the emergence for Hopf bifurcation are derived. The period doubling route to chaos behaviors of such a system is discussed by using a bifurcation diagram, a phase diagram, a time-domain diagram, and the largest Lyapunov exponents (LLEs) diagram. Specifically, we study the influence of time delay on the chaotic behavior, and find that when time delay increases, the transitions from one cycle to two cycles, two cycles to four cycles, and four cycles to chaos are observed in this system model. Corresponding critical values of time delay are determined, showing the lowest orders for chaos in the fractional-order delayed memristive system. Finally, numerical simulations are provided to verify the correctness of theoretical analysis using the modified Adams–Bashforth–Moulton method.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleNonlinear Dynamic Analysis of a Simplest Fractional-Order Delayed Memristive Chaotic System
    typeJournal Paper
    journal volume12
    journal issue4
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.4035412
    journal fristpage41003
    journal lastpage041003-8
    treeJournal of Computational and Nonlinear Dynamics:;2017:;volume( 012 ):;issue: 004
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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