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Based on the traveling wave theory, a nonlinear discrete map of a transmission line system terminated by an N-channel metal oxide semiconductor (NMOS) inverter is established. After simulating by the nonlinear discrete map, it is found that the change of the reflection coefficient may lead to spatiotemporal bifurcation and chaos, and that the initial distribution significantly affects the spatiotemporal pattern of steady state. For the zero initial distribution, the spatiotemporal pattern is very regular, whereas the complex spatiotemporal pattern may appear when the initial distribution is nonzero. The analysis results demonstrate that the complex spatiotemporal behaviors originate from the infinite-dimensional essence of the transmission line and the nonlinear voltage-ampere characteristics of the NMOS inverter.
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Keywords:
- transmission line /
- NMOS inverter /
- bifurcation /
- spatiotemporal chaos
[1] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2] Cross M C, Hohenberg P C 1994 Science 263 1569
[3] Chacon R, Marcheggiani L 2010 Phys. Rev. E 82 016201
[4] Miranda M A, Burguete J 2009 Phys. Rev. E 79 046201
[5] Neubecker R, Gutlich B 2004 Phys. Rev. Lett. 92 154101
[6] Yue L J, Shen K, Xu M Q 2007 Acta Phys. Sin. 56 4378 (in Chinese) [岳立娟, 沈柯, 徐明奇 2007 物理学报 56 4378]
[7] Krefting D, Kaira P, Rotermund H H 2009 Phys. Rev. Lett. 102 178301
[8] Wang X Y, Zhang N 2010 Chin. Phys. B 19 090504
[9] Lv L, Xia X L 2009 Acta Phys. Sin. 58 814 (in Chinese) [吕翎, 夏晓岚 2009 物理学报 58 814]
[10] Stahlke D, Wackerbauer R 2011 Phys. Rev. E 83 046204
[11] Rucklidge A M, Silber M, Skeldon A C 2012 Phys. Rev. Lett. 108 074504
[12] Ahlborn A, Parlitz U 2008 Phys. Rev. E 77 016201
[13] Jin Y H, Xu Z Y 2011 Chin. Phys. B 20 120505
[14] Kaneko K 1989 Physica D 37 60
[15] Muruganandam P, Francisco G, Menezes M de, Ferreira F F 2009 Chaos Soliton. Fract. 41 997
[16] Lü L, Li G, Chai Y 2008 Acta Phys. Sin. 57 7517 (in Chinese) [吕翎, 李钢, 柴元 2008 物理学报 57 7517]
[17] Ayers J E 2010 Digital Integrated Circuits Analysis and Design (2nd Ed.) (New York: CRC Press) p201
[18] Hall S H, Hall G W, McCall J A 2008 High-Speed Digital System Design (New York: John Wiley & Sons, Inc.) p14
[19] Lee J, Lee S, Nam S 2011 IEEE Trans. Electromagn. C 53 366
[20] Tang M, Ma X K 2004 Acta Electronica Sin. 32 787 (in Chinese) [唐旻, 马西奎 2004 电子学报 32 787]
[21] Sharkovsky A N 1993 IEEE Trans. Circ. Syst. I 40 781
[22] Zou J L, Chen F, Ma X K 2010 Int. J. Appl. Electrom. 33 369
[23] Ma X K, Yang M, Zou J L, Wang L T 2006 Acta Phys. Sin. 55 5648 (in Chinese) [马西奎, 杨梅, 邹建龙, 王玲桃 2006 物理学报 55 5648]
[24] Wang L T, Ma X K, Zou J L, Yang M 2006 Acta Phys. Sin. 55 5647 (in Chinese) [王玲桃, 马西奎, 邹建龙, 杨梅 2006 物理学报 55 5657]
[25] Corti L, De Menna L, Miano G, Verolino L 1994 IEEE Trans. Circ. Syst. I 41 730
[26] Wang L T, Ma X K 2008 IEEE Trans. Circ. Syst. I 55 1125
[27] Blakely J N, Corron N J 2004 Chaos 14 1035
[28] Paul C R 2008 Analysis of Multiconductor Transmission Lines (2nd Ed.) (New Jersey: John Wiley & Sons, Inc.) p344
[29] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p538 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学(北京:高等教育出版社) 第538页]
[30] Nakhla N, Nakhla M, Achar R 2011 IEEE Trans. Microw. Theory 59 46
[31] Zhao Y H, Chen J N, Wu X L, Mei Z F, Xu T L, Lu S B 2008 Comput. Tech. Dev. 18 170 (in Chinese) [赵宇浩, 陈军宁, 吴秀龙, 梅振飞, 徐太龙, 鲁士滨 2008 计算机技术与发展 18 170]
[32] Maas S A 2003 Nonlinear Microwave and RF circuits (London: Artech House) p7
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[1] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2] Cross M C, Hohenberg P C 1994 Science 263 1569
[3] Chacon R, Marcheggiani L 2010 Phys. Rev. E 82 016201
[4] Miranda M A, Burguete J 2009 Phys. Rev. E 79 046201
[5] Neubecker R, Gutlich B 2004 Phys. Rev. Lett. 92 154101
[6] Yue L J, Shen K, Xu M Q 2007 Acta Phys. Sin. 56 4378 (in Chinese) [岳立娟, 沈柯, 徐明奇 2007 物理学报 56 4378]
[7] Krefting D, Kaira P, Rotermund H H 2009 Phys. Rev. Lett. 102 178301
[8] Wang X Y, Zhang N 2010 Chin. Phys. B 19 090504
[9] Lv L, Xia X L 2009 Acta Phys. Sin. 58 814 (in Chinese) [吕翎, 夏晓岚 2009 物理学报 58 814]
[10] Stahlke D, Wackerbauer R 2011 Phys. Rev. E 83 046204
[11] Rucklidge A M, Silber M, Skeldon A C 2012 Phys. Rev. Lett. 108 074504
[12] Ahlborn A, Parlitz U 2008 Phys. Rev. E 77 016201
[13] Jin Y H, Xu Z Y 2011 Chin. Phys. B 20 120505
[14] Kaneko K 1989 Physica D 37 60
[15] Muruganandam P, Francisco G, Menezes M de, Ferreira F F 2009 Chaos Soliton. Fract. 41 997
[16] Lü L, Li G, Chai Y 2008 Acta Phys. Sin. 57 7517 (in Chinese) [吕翎, 李钢, 柴元 2008 物理学报 57 7517]
[17] Ayers J E 2010 Digital Integrated Circuits Analysis and Design (2nd Ed.) (New York: CRC Press) p201
[18] Hall S H, Hall G W, McCall J A 2008 High-Speed Digital System Design (New York: John Wiley & Sons, Inc.) p14
[19] Lee J, Lee S, Nam S 2011 IEEE Trans. Electromagn. C 53 366
[20] Tang M, Ma X K 2004 Acta Electronica Sin. 32 787 (in Chinese) [唐旻, 马西奎 2004 电子学报 32 787]
[21] Sharkovsky A N 1993 IEEE Trans. Circ. Syst. I 40 781
[22] Zou J L, Chen F, Ma X K 2010 Int. J. Appl. Electrom. 33 369
[23] Ma X K, Yang M, Zou J L, Wang L T 2006 Acta Phys. Sin. 55 5648 (in Chinese) [马西奎, 杨梅, 邹建龙, 王玲桃 2006 物理学报 55 5648]
[24] Wang L T, Ma X K, Zou J L, Yang M 2006 Acta Phys. Sin. 55 5647 (in Chinese) [王玲桃, 马西奎, 邹建龙, 杨梅 2006 物理学报 55 5657]
[25] Corti L, De Menna L, Miano G, Verolino L 1994 IEEE Trans. Circ. Syst. I 41 730
[26] Wang L T, Ma X K 2008 IEEE Trans. Circ. Syst. I 55 1125
[27] Blakely J N, Corron N J 2004 Chaos 14 1035
[28] Paul C R 2008 Analysis of Multiconductor Transmission Lines (2nd Ed.) (New Jersey: John Wiley & Sons, Inc.) p344
[29] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p538 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学(北京:高等教育出版社) 第538页]
[30] Nakhla N, Nakhla M, Achar R 2011 IEEE Trans. Microw. Theory 59 46
[31] Zhao Y H, Chen J N, Wu X L, Mei Z F, Xu T L, Lu S B 2008 Comput. Tech. Dev. 18 170 (in Chinese) [赵宇浩, 陈军宁, 吴秀龙, 梅振飞, 徐太龙, 鲁士滨 2008 计算机技术与发展 18 170]
[32] Maas S A 2003 Nonlinear Microwave and RF circuits (London: Artech House) p7
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