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Owing to the limitations of the concept of frequency for power spectrum and the inherent defects of Fourier transform, a novel concept of general local frequency is proposed. Based on a approach to adaptive peak decomposition, the dynamic feature in frequency domain varying with parameter r of Duffing system driven by periodic signal is investigated. And a phenomenon of frequency bifurcation is found. Moreover, coninuous frequency bands exist near the central frequency of chaos time seriers at different values of parameter r and their shapes are similar. By demodulation analysis of Hilbert transform, the modulation characteristic and modulation similarity of chaos time seriers are summarized. The above study shows that the proposed approach to general local frequency based on adaptive peak is effective for freature extraction in frequency domain of Duffing system. It provides a new method to observe a continunous distribution of frequency bands for the non-linear system in chaotic state.
[1] Zhou X Y 2011 Acta Phys. Sin. 60 010503 (in Chinese) [周小勇 2011 物理学报 60 10503]
[2] Lv J H, Lu J A, Chen S H 2005 Analysis and Aplication of Chaos Time Seriers (1st ed) (Wuhan: Wuhan University Press) p47 (in Chinese) [吕金虎, 陆君安, 陈士华 2005 混沌时间序列分析及其应用(第1版) 第47页]
[3] Thamilmaran K, Senthilkumar D, Venkatesan A, Lakshmanan M 2006 Phys. Rev. E 74 036205
[4] Eduardo G Altmann, Tamás Tél 2009 Phys. Rev. E 79 016204
[5] Parthasarathy S, Manikandakumar K 2010 Chaos 20 039901
[6] Qin W Y, Meng G, Zhang T 2003 Journal of Sound and Vibration 259 571
[7] Afsar Ozgur, Tirnakli Ugur 2010 Phys. Rev. E 82 046210
[8] Pierre-Francois Loos, Peter M W Gill 2010 Phys Rev. Lett. 105 113001
[9] Mohammad Ataei, Arash Kiyoumarsi, Behzad Ghorbani 2010 Phys. Lett. A 374 4226
[10] Zhou Y H 2010 Acta Methematica Scientia 31 102
[11] Li Y G, Liu J, Zhang J P 2008 Chinese Journal of Mechanical Engineering. 44 82 (in Chinese) [李允公, 刘杰, 张金萍 2008 机械工程学报 40 82]
[12] Anthony Challinor, Antony Lewis 2011 Phys. Rev. D 84 043516
[13] Relaño A, Muñoz L, Retamosa J, Faleiro E, Molina R A 2008 Phys. Rev. E 77 031103
[14] Nikitin A, Stocks N G, Bulsara A R 2007 Phys. Rev. E 76 041138
[15] Ogawa Jun, Tanaka Hiroaki 2009 Probabilistic Engineering Mechanics 24 537
[16] Babu H, Wanare Harshawardhan 2011 Phys. Rev. A 83 033819
[17] Gong Y B 2011 Phys. A 390 3662
[18] Hu Y H, Ma Z Y 2007 Chaos, Solitons & Fractals 34 482
[19] Braun S, Feldman M 2011 Mechanical Systems and Signal Processing 25 072608
[20] Jonathan M L, Sofia C O Bivariate 2010 IEEE Transactions on Signal Processing 58 591
[21] Laila D S, Messina A R, Pal B C A 2009 IEEE Transaction on Power Systems 24 610
[22] Gong Z Q, Zou M W, Gao X Q, Dong W J 2005 Acta Phys. Sin. 54 3947 (in Chinese) [龚志强, 邹明玮, 高新全, 董文杰 2005 物理学报 54 3947]
[23] Wang K, Guang X P, Ding X F, Qiao J M 2010 Acta Phys. Sin. 59 6859 (in Chinese) [王坤, 关新平, 丁喜峰, 乔杰敏 2010 物理学报 59 6859]
[24] Yang M, An J P, Chen N, Wei J C 2011 Transactions of Beijing Institute of Technology 31 329 (in Chinese) [杨淼, 安建平, 陈宁, 卫景宠 2011 北京理工大学学报 31 329]
[25] Hartley R, Zisserman A 2003 Multiple View Geometry in Computer Vision (2nd ed) (New York: Cambridge University Press) p95
[26] Ma S D, Zhang Z Y 2003 Computer Vision-Computation Theory and Algorithm Fundamentals (Beijing: Science Press) p67 (in Chinese) [马颂德, 张正友 2003 计算机视觉-计算理论和算法基础(北京:科学出版社) 第67页]
[27] Feldman M 2011 Mechanical Systems and Signal Processing 25 3205
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[1] Zhou X Y 2011 Acta Phys. Sin. 60 010503 (in Chinese) [周小勇 2011 物理学报 60 10503]
[2] Lv J H, Lu J A, Chen S H 2005 Analysis and Aplication of Chaos Time Seriers (1st ed) (Wuhan: Wuhan University Press) p47 (in Chinese) [吕金虎, 陆君安, 陈士华 2005 混沌时间序列分析及其应用(第1版) 第47页]
[3] Thamilmaran K, Senthilkumar D, Venkatesan A, Lakshmanan M 2006 Phys. Rev. E 74 036205
[4] Eduardo G Altmann, Tamás Tél 2009 Phys. Rev. E 79 016204
[5] Parthasarathy S, Manikandakumar K 2010 Chaos 20 039901
[6] Qin W Y, Meng G, Zhang T 2003 Journal of Sound and Vibration 259 571
[7] Afsar Ozgur, Tirnakli Ugur 2010 Phys. Rev. E 82 046210
[8] Pierre-Francois Loos, Peter M W Gill 2010 Phys Rev. Lett. 105 113001
[9] Mohammad Ataei, Arash Kiyoumarsi, Behzad Ghorbani 2010 Phys. Lett. A 374 4226
[10] Zhou Y H 2010 Acta Methematica Scientia 31 102
[11] Li Y G, Liu J, Zhang J P 2008 Chinese Journal of Mechanical Engineering. 44 82 (in Chinese) [李允公, 刘杰, 张金萍 2008 机械工程学报 40 82]
[12] Anthony Challinor, Antony Lewis 2011 Phys. Rev. D 84 043516
[13] Relaño A, Muñoz L, Retamosa J, Faleiro E, Molina R A 2008 Phys. Rev. E 77 031103
[14] Nikitin A, Stocks N G, Bulsara A R 2007 Phys. Rev. E 76 041138
[15] Ogawa Jun, Tanaka Hiroaki 2009 Probabilistic Engineering Mechanics 24 537
[16] Babu H, Wanare Harshawardhan 2011 Phys. Rev. A 83 033819
[17] Gong Y B 2011 Phys. A 390 3662
[18] Hu Y H, Ma Z Y 2007 Chaos, Solitons & Fractals 34 482
[19] Braun S, Feldman M 2011 Mechanical Systems and Signal Processing 25 072608
[20] Jonathan M L, Sofia C O Bivariate 2010 IEEE Transactions on Signal Processing 58 591
[21] Laila D S, Messina A R, Pal B C A 2009 IEEE Transaction on Power Systems 24 610
[22] Gong Z Q, Zou M W, Gao X Q, Dong W J 2005 Acta Phys. Sin. 54 3947 (in Chinese) [龚志强, 邹明玮, 高新全, 董文杰 2005 物理学报 54 3947]
[23] Wang K, Guang X P, Ding X F, Qiao J M 2010 Acta Phys. Sin. 59 6859 (in Chinese) [王坤, 关新平, 丁喜峰, 乔杰敏 2010 物理学报 59 6859]
[24] Yang M, An J P, Chen N, Wei J C 2011 Transactions of Beijing Institute of Technology 31 329 (in Chinese) [杨淼, 安建平, 陈宁, 卫景宠 2011 北京理工大学学报 31 329]
[25] Hartley R, Zisserman A 2003 Multiple View Geometry in Computer Vision (2nd ed) (New York: Cambridge University Press) p95
[26] Ma S D, Zhang Z Y 2003 Computer Vision-Computation Theory and Algorithm Fundamentals (Beijing: Science Press) p67 (in Chinese) [马颂德, 张正友 2003 计算机视觉-计算理论和算法基础(北京:科学出版社) 第67页]
[27] Feldman M 2011 Mechanical Systems and Signal Processing 25 3205
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