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
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中南大學(xué)物理與電子學(xué)院 長(zhǎng)沙 410006
Characteristics Analysis and DSP Implementation of Fractional-order Memristive Hypogenetic Jerk System
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School of Physics and Electronics, Central South University, Changsha 410006, China
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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。
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關(guān)鍵詞:
- 憶阻器 /
- 混沌 /
- 分?jǐn)?shù)階微積分 /
- 吸引子共存 /
- 多穩(wěn)態(tài)
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.-
Key words:
- Memristor /
- Chaos /
- Fractional calculus /
- Coexistence attractors /
- Multistability
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