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In this paper, firstly according to the basic characteristics of chaos theory, we establish the nonlinear enlarge model about tent map, especially the initial-value sensitive dependence and one-to-one correspondence between chaotic orbit and the initial value. Secondly, we study the concrete characteristics with which the tent mapping system can realize nonlinear amplification. And the binary relationship between input and output is analyzed. Then we make numerical and circuit simulations of nonlinear amplification of the sine signal and the sine signal with noise. We compare the results of linear amplification and nonlinear amplification by tent mapping. At last, the advantages and disadvantages of the realized situations are discussed. The simulation results proved the superiority of the weak signal nonlinear amplification method.
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Keywords:
- chaos /
- tent mapping /
- nonlinear amplifying /
- circuit simulation
[1] ［1］Huang J, Pei W J, Liu W B, Yu S L 1997 Transactions of Nanjing University of Aeronautics & Astronautics 29 295(in Chinese)［黄靖、裴文江、刘文波、于盛林 1997南京航空航天大学学报 29 295］
[2] ［2］Huang W G, Jin M, Tong Q Y 2000 Chinese Science Abstracts 6 248 (in Chinese)［黄文高、金敏、童勤业 2000 中国学术期刊文摘（科技快报）6 248］
[3] ［3］Litovski Vanco,Aadrejevic Miona,Nikolic Miljan 2006 Neural Network Applications in Electrical Engineering 173
[4] ［4］Ren H P, Liu D 2007 Journal of Scientific Instrument 28 42(in Chinese)［任海鹏、刘丁 2007 仪器仪表学报28 42］
[5] ［5］Hao J H, Ding W, Zhang Z C 2003 Acta Phys.Sin. 52 1979(in Chinese)［郝建红、丁武、张治畴 2003 物理学报 52 1979］
[6] ［6］Wang L Z, Zhao W L 2005 Acta Phys.Sin. 54 4038(in Chinese)［王林泽、赵文礼 2005物理学报 54 4038］
[7] ［7］Wang F P, Wang Z J, Guo J B 2002 Acta Phys.Sin. 51 474 (in Chinese)［ 王芙平、王赞基、郭静波 2002 物理学报 51 474］
[8] ［8］Wang G Y, Yu J B, Gu T X 2001 Acta Phys.Sin. 50 2307(in Chinese)［王改云、虞厥邦、古天祥 2001 物理学报 50 2307］
[9] ［9］Lu J G,Xi Y G 2005 Chin. Phys. 14 274
[10] ］Shen M F, Lin L X, Li X Y, Chang C Q 2009 Acta Phys.Sin. 58 2921 (in Chinese) ［沈民奋、 林兰馨、 李小艳、 常春起 2009物理学报 58 2921］
[11] ］Liu S D, Liang F M, Liu S S, Xin G J 2003 Chaos and Fractal in Nature (Press of Peking University)p21［刘式达、梁福明、刘式适、辛国君 2003 自然科学中的混沌和分形（北京大学出版社）第21页］
[12] ］Zheng W M, Hao B L 1994 Applied Symbolic Dynamics(Shanghai Scientific and Technological Education Publishing House)p45［郑伟谋、郝柏林 1994 实用符号动力学(上海科技教育出版社)第45页］
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[1] ［1］Huang J, Pei W J, Liu W B, Yu S L 1997 Transactions of Nanjing University of Aeronautics & Astronautics 29 295(in Chinese)［黄靖、裴文江、刘文波、于盛林 1997南京航空航天大学学报 29 295］
[2] ［2］Huang W G, Jin M, Tong Q Y 2000 Chinese Science Abstracts 6 248 (in Chinese)［黄文高、金敏、童勤业 2000 中国学术期刊文摘（科技快报）6 248］
[3] ［3］Litovski Vanco,Aadrejevic Miona,Nikolic Miljan 2006 Neural Network Applications in Electrical Engineering 173
[4] ［4］Ren H P, Liu D 2007 Journal of Scientific Instrument 28 42(in Chinese)［任海鹏、刘丁 2007 仪器仪表学报28 42］
[5] ［5］Hao J H, Ding W, Zhang Z C 2003 Acta Phys.Sin. 52 1979(in Chinese)［郝建红、丁武、张治畴 2003 物理学报 52 1979］
[6] ［6］Wang L Z, Zhao W L 2005 Acta Phys.Sin. 54 4038(in Chinese)［王林泽、赵文礼 2005物理学报 54 4038］
[7] ［7］Wang F P, Wang Z J, Guo J B 2002 Acta Phys.Sin. 51 474 (in Chinese)［ 王芙平、王赞基、郭静波 2002 物理学报 51 474］
[8] ［8］Wang G Y, Yu J B, Gu T X 2001 Acta Phys.Sin. 50 2307(in Chinese)［王改云、虞厥邦、古天祥 2001 物理学报 50 2307］
[9] ［9］Lu J G,Xi Y G 2005 Chin. Phys. 14 274
[10] ］Shen M F, Lin L X, Li X Y, Chang C Q 2009 Acta Phys.Sin. 58 2921 (in Chinese) ［沈民奋、 林兰馨、 李小艳、 常春起 2009物理学报 58 2921］
[11] ］Liu S D, Liang F M, Liu S S, Xin G J 2003 Chaos and Fractal in Nature (Press of Peking University)p21［刘式达、梁福明、刘式适、辛国君 2003 自然科学中的混沌和分形（北京大学出版社）第21页］
[12] ］Zheng W M, Hao B L 1994 Applied Symbolic Dynamics(Shanghai Scientific and Technological Education Publishing House)p45［郑伟谋、郝柏林 1994 实用符号动力学(上海科技教育出版社)第45页］
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