離散動力系統(tǒng)無退化-配置N個正Lyapunov指數(shù)
doi: 10.11999/JEIT180925
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1.
西安電子科技大學(xué)? ?西安? ?710071
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2.
北京電子科技學(xué)院? ?北京? ?100070
基金項目: 國家自然科學(xué)基金(61772047)
Discrete Dynamic System without Degradation -configure N Positive Lyapunov Exponents
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1.
Xidian University, Xi’an 710071, China
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2.
Beijing Electronic Science and Technology Institute, Beijing 100070, China
Funds: The National Natural Science Foundation of China(61772047)
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摘要: 針對離散時間混沌動力學(xué)系統(tǒng)，該文提出一種基于矩陣特征值以及特征向量配置Lyapunov指數(shù)為正的新算法。計算離散受控矩陣的特征值以及特征向量，設(shè)計一類具有正Lyapunov指數(shù)的通用控制器，理論證明系統(tǒng)軌道的有界性和Lyapunov指數(shù)的有限性。對線性反饋算子以及微擾反饋算子進行數(shù)值仿真分析，驗證了算法的正確性、通用性和有效性。性能評估表明，與Chen-Lai算法相比，該方法可以構(gòu)建較低計算復(fù)雜度的混沌系統(tǒng)，并且運行時間較短，其輸出序列也具有較強的隨機性，實現(xiàn)了無退化、無兼并的離散混沌系統(tǒng)。
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關(guān)鍵詞:
- 混沌系統(tǒng) /
- 無退化 /
- Lyapunov指數(shù) /
- 矩陣特征值 /
- 線性反饋算子 /
- 微擾反饋算子
Abstract: Considering discrete-time chaotic dynamics systems, a new algorithm is proposed which is based on matrix eigenvalues and eigenvectors to configure Lyapunov exponents to be positive. The eigenvalues and eigenvectors of the discrete controlled matrix are calculated to design a general controller with positive Lyapunov exponents. The theory proves the boundedness of the system orbit and the finiteness of the Lyapunov exponents. The numerical simulation analysis of the linear feedback operator and the perturbation feedback operator verifies the correctness, versatility and effectiveness of the algorithm. Performance evaluations show that, compared with Chen-Lai methods, the proposed method can construct chaotic system with lower computation complexity and the running time is shorter and the outputs demonstrate strong randomness. Thus, a discrete chaotic system with no degradation and no merger is realized. -
表 1 兩種算法配置Lyapunov指數(shù)效果比較
期望配置的李氏指數(shù) Chen-Lai算法 本文算法 0.1 1.4112; 1.8741 0.1261; 0.1101 0.6 1.5732; 1.9542 0.6612; 0.6213 3.0 3.1392; 3.2317 3.0201; 3.0131 
下載: 導(dǎo)出CSV
表 2 2種算法運行速度的比較(s)
混沌系統(tǒng)的維數(shù) Chen-Lai算法 本文算法 3 0.0517 0.0279 4 0.0579 0.0287 5 0.1025 0.0587 6 0.1534 0.6640
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