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分?jǐn)?shù)階憶阻退化Jerk系統(tǒng)的特性分析與DSP實(shí)現(xiàn)

孫克輝,  秦川,  王會(huì)海

孫克輝, 秦川, 王會(huì)海. 分?jǐn)?shù)階憶阻退化Jerk系統(tǒng)的特性分析與DSP實(shí)現(xiàn)[J]. 電子與信息學(xué)報(bào), 2020, 42(4): 888-894. doi: 10.11999/JEIT190904
引用本文: 孫克輝, 秦川, 王會(huì)海. 分?jǐn)?shù)階憶阻退化Jerk系統(tǒng)的特性分析與DSP實(shí)現(xiàn)[J]. 電子與信息學(xué)報(bào), 2020, 42(4): 888-894. doi: 10.11999/JEIT190904
Kehui SUN, Chuan QIN, Huihai WANG. Characteristics Analysis and DSP Implementation of Fractional-order Memristive Hypogenetic Jerk System[J]. Journal of Electronics & Information Technology, 2020, 42(4): 888-894. doi: 10.11999/JEIT190904
Citation: Kehui SUN, Chuan QIN, Huihai WANG. Characteristics Analysis and DSP Implementation of Fractional-order Memristive Hypogenetic Jerk System[J]. Journal of Electronics & Information Technology, 2020, 42(4): 888-894. doi: 10.11999/JEIT190904

分?jǐn)?shù)階憶阻退化Jerk系統(tǒng)的特性分析與DSP實(shí)現(xiàn)

doi: 10.11999/JEIT190904

  • 中南大學(xué)物理與電子學(xué)院 長(zhǎng)沙 410006

詳細(xì)信息
    作者簡(jiǎn)介:

    孫克輝：男，1968年生，教授，博士生導(dǎo)師，主要研究方向?yàn)榛煦缋碚撆c應(yīng)用、非線(xiàn)性電路與系統(tǒng)

    秦川：男，1996年生，碩士生，主要研究方向?yàn)榛煦鐒?dòng)力學(xué)分析，分?jǐn)?shù)階混沌系統(tǒng)與應(yīng)用

    王會(huì)海：男，1978年生，博士，副教授，主要研究方向?yàn)榛煦缋碚摷捌鋺?yīng)用、嵌入式系統(tǒng)應(yīng)用

    通訊作者:

    孫克輝　kehui@csu.edu.cn

  • 中圖分類(lèi)號(hào): TN601

Characteristics Analysis and DSP Implementation of Fractional-order Memristive Hypogenetic Jerk System

  • School of Physics and Electronics, Central South University, Changsha 410006, China

  • 摘要: 為了探究分?jǐn)?shù)階形式下該類(lèi)系統(tǒng)的動(dòng)力學(xué)特性，該文將分?jǐn)?shù)階微積分引入到憶阻退化Jerk系統(tǒng)中，增加了一個(gè)自由度，提升了系統(tǒng)性能。通過(guò)相圖、分岔圖、李雅普諾夫指數(shù)譜、復(fù)雜度混沌圖等分析了系統(tǒng)的動(dòng)力學(xué)特性，并采用DSP技術(shù)，實(shí)現(xiàn)了該系統(tǒng)的數(shù)字電路。研究結(jié)果表明，系統(tǒng)拓展到分?jǐn)?shù)階后有兩種不同的單渦卷吸引子，系統(tǒng)隨初值變化呈現(xiàn)倍周期分岔路徑，在某些特定初值處系統(tǒng)演化路徑出現(xiàn)躍變。系統(tǒng)具有無(wú)限多個(gè)吸引子共存。
    Abstract: To investigate the dynamic characteristics of this type of system in the fractional-order case, fractional-order calculus is introduced into memristive hypogenetic Jerk system, which adds one degree of freedom and improves system performance. The dynamical characteristics of the system are analyzed by phase diagram, bifurcation diagram, Lyapunov exponent spectrum, complexity chaotic diagram, etc., and the digital circuit of the system is realized by employing DSP technology. The research results show that when the system is extended to the fractional order, the system presents a period doubling bifurcation path with the initial value, and the evolution path of the system changes abruptly at some specific initial values, showing infinite coexistence of attractors.
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  • 圖  1  系統(tǒng)式(1)不同平面的吸引子相圖

    圖  2  不同階數(shù)下的吸引子相圖

    圖  3  系統(tǒng)階數(shù)q變化時(shí)的動(dòng)力學(xué)特性

    圖  4  系統(tǒng)參數(shù)a變化時(shí)的動(dòng)力學(xué)特性

    圖  5  系統(tǒng)參數(shù)b變化時(shí)的動(dòng)力學(xué)特性

    圖  6  系統(tǒng)參數(shù)a-b平面SE復(fù)雜度混沌圖

    圖  7  系統(tǒng)初值y(0)變化時(shí)的動(dòng)力學(xué)特性

    圖  8  系統(tǒng)初值w(0)變化時(shí)的動(dòng)力學(xué)特性

    圖  9  系統(tǒng)初值y(0)-w(0)平面SE復(fù)雜度混沌圖

    圖  10  分?jǐn)?shù)階式(3)系統(tǒng)的多吸引子共存現(xiàn)象

    圖  11  不同初值下系統(tǒng)式(1)電路實(shí)驗(yàn)相圖

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出版歷程
  • 收稿日期:  2019-11-13
  • 修回日期:  2020-02-13
  • 網(wǎng)絡(luò)出版日期:  2020-03-10
  • 刊出日期:  2020-06-04

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