簡(jiǎn)潔無(wú)電感憶阻混沌電路及其特性
doi: 10.11999/JEIT190859
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湘潭大學(xué)物理與光電工程學(xué)院 湘潭 411105
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61471310)
A Simple Inductor-free Memristive Chaotic Circuit and Its Characteristics
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School of Physics and Photoelectric Engineering, Xiangtan University, Xiangtan, 411105, China
Funds: The National Natural Science Foundation of China (61471310)
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摘要: 采用非理想有源電壓控制憶阻器和磁通控制型光滑3次非線(xiàn)性憶阻器,該文設(shè)計(jì)了一種不含電感的簡(jiǎn)單(只含5個(gè)電子元器件)雙憶阻混沌電路。采用常規(guī)的非線(xiàn)性分析手段詳細(xì)研究了電路參數(shù)變化時(shí)系統(tǒng)的基本動(dòng)力學(xué)行為,例如平衡點(diǎn)穩(wěn)定性分析,相軌圖以及李雅普諾夫指數(shù)譜和分岔圖等。通過(guò)調(diào)節(jié)系統(tǒng)控制參數(shù),該系統(tǒng)可產(chǎn)生多渦卷、多翼以及暫態(tài)混沌等十分豐富的動(dòng)力學(xué)現(xiàn)象。此外,還研究了系統(tǒng)依賴(lài)于憶阻器初始狀態(tài)的多穩(wěn)態(tài),得到了一些有意義的結(jié)果。為驗(yàn)證電路的可行性及穩(wěn)定性,通過(guò)對(duì)憶阻器的模擬等效電路的搭建,并將該等效電路應(yīng)用于所提出的混沌電路中,硬件電路實(shí)驗(yàn)結(jié)果以及Multisim電路仿真結(jié)果與理論分析一致。
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關(guān)鍵詞:
- 憶阻器 /
- 混沌電路 /
- 多穩(wěn)態(tài) /
- 暫態(tài)混沌
Abstract: A simple two-memristor chaotic circuit without inductance (only five electronic components) is designed by using a non-ideal active voltage control memristor and a flux-controlled smooth cubic nonlinear memristor. When the circuit parameters change, the basic dynamic behaviors of the system are studied in detail by the means of conventional nonlinear analysis, such as the analysis of equilibrium stability, phase diagram, Lyapunov exponent spectrum and bifurcation diagram. With the parameters changing, the proposed system can produce various phenomena of dynamics such as multi-scrolls, multi-wings and transient transition behaviors. Furthermore, the multistability characteristics of the system are also studied in the condition of changing the initial state of two memristors in system respectively, and some meaningful results are obtained. In order to verify the feasibility and stability of the circuit, the analog equivalent circuit of each memristor is constructed, and it is applied to the proposed chaotic circuit. The experimental results of the hardware circuit and the circuit simulation results of the Multisim are in good agreement with the theoretical analysis.-
Key words:
- Memristor /
- Chaotic circuit /
- Multistability /
- Transient transition behaviors
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表 1 憶阻器W3隨初始狀態(tài)變化所產(chǎn)生的多穩(wěn)態(tài)舉例
z(0)取值 LE李雅普諾夫指數(shù) 系統(tǒng)狀態(tài) 4.0 (+, 0, –, –) 2翼混沌吸引子 6.5 (+, 0, –, –) 4翼混沌吸引子 13.5 (+, 0, –, –) 6翼混沌吸引子 17.5 (+, 0, –, –) 8翼混沌吸引子 下載: 導(dǎo)出CSV
表 2 簡(jiǎn)潔無(wú)電感憶阻混沌電路的參數(shù)取值
參數(shù) 名稱(chēng) 參值 $ {C_a},{C_1},{C_3}$ 電容 1 nF C2 電容 25 nF $ {g_a},{\rm{ }}{g_b},{\rm{ }}{g_{3,}}{g_4}$ 增益 1 $ {g_1},{\rm{ }}{g_2}$ 增益 0.1 R1 電阻 0.25 kΩ R2 電阻 50.00 kΩ R3 電阻 25.00 kΩ $ {R_4},{\rm{ }}{R_c}$ 電阻 10.00 kΩ Rb 電阻 16.70 kΩ $ {R_d},{R_e}_,{R_5}{,}{R_6}$ 電阻 2.00 kΩ 下載: 導(dǎo)出CSV
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