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In this paper, the action exerted by a superlattice sawtooth-shaped channel on the particle is assumed to be equivalent to that exerted by a periodic field with a similar shape. In the framework of classical mechanics, by introducing the sines-quared potential, the particle motion equation is reduced to pendulum equation with a damping term and dual-frequency excitation term. The bifurcation and chaos of single-frequency excitation system are analyzed with the Melnikov method. The stability of dual-frequency excitation system is discussed by using the Lyapunov exponent. The results show that in the case of weak nonlinearity, local instability can be found in the dual frequency excitation system, and it will be expanded globally until chaos appears. The dual excitation intensity leading to chaos is far less than that of single-frequency excitation. The application of an appropriate ultrasonic field is likely to make such a sensitivity passivated, and the stability of the system improved as well.
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Keywords:
- superlattice /
- quasi-periodic excitation /
- chaos /
- stabilities
[1] Korol A V, Solovyov A V, Greiner W 2004 Int. J. Mod. Phys. E 13 867
[2] Korol A V, Solovyov A V, Greiner W 2008 Nucl. Inst. Meth. Phys. Res. B 266 1173
[3] Kubankin A S, Nasonov N N 2008 J. Surf. Investig. X Ra. 2 317
[4] Tabrizi M, Korol A V, Solovyov A V 2007 Phys. Rev. Lett. 98 164801
[5] Korol A V, Solovyov A V, Greiner W 2007 Int. J. Mod. Phys. E 13 867
[6] Sushko G B, Korol A V, Greiner W, Solov’yov A V 2013 J. Phys.: Conf. Ser. 438 012018
[7] Korol A V, Solov’yov A V, Greiner W 2013 Channeling and Radiation in Periodically Bent Crystals, Springer Series on Atomic, Optical, and Plasma Physics (Berlin: Splinger) p195
[8] Gennady B S, Bezchastnov V G, Solovyov I A, Korol A V, Greiner W, Solovyov A V 2013 J. Comput. Phys. 252 404
[9] Luo S Y, Shao M Z, Luo X H 2010 Sci. China: Phys. Mech. Astron. 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学: 物理学, 力学和天文学 40 207]
[10] Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin. 59 2685 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 59 2685]
[11] Luo X H, Wu M Y, Li H T, Shao M Z, Xiong J Z, Luo S Y, He W 2011 Chin. J. Solid Mech. 32 440 (in Chinese) [罗晓华, 吴木营, 李洪涛, 邵明珠, 熊金志, 罗诗裕, 何为 2011 固体力学学报 32 440]
[12] Luo X H, He W, Shao M Z 2008 High Power Laser and Particle Beams 20 675 (in Chinese) [罗晓华, 何为, 邵明珠 2008 强激光与粒子束 20 675]
[13] Luo S Y, Shao M Z 2005 Chin. J. Seimcond. 26 294 (in Chinese) [罗诗裕, 邵明珠 2005 半导体学报 26 294]
[14] Li X P, Wang S J, Chen Q, Luo S Y 2013 Seim. Optoelectron. 34 441 (in Chinese) [李秀平, 王善进, 陈琼, 罗诗裕 2013 半导体光电 34 441]
[15] Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[16] Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[17] Nayfeh A H 1981 Introduction to Peturbation Techniques (London: John Wiley and Sons.) p226
[18] Grishchenko A D, Vavriv D M 1997 Zh. Tekh. Fiz. 67 1 (in Russia)
[19] Vavriv D M, Vavriv D D 2008 Proceedings of Ultrawideband and Ultrashort Impulse Signals Sevastopol, Ukraine, September 15–19, 2008 p16
[20] Wolf A, Swift J B, Vastano J A, Sminney H L 1985 Physica D 16 285
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[1] Korol A V, Solovyov A V, Greiner W 2004 Int. J. Mod. Phys. E 13 867
[2] Korol A V, Solovyov A V, Greiner W 2008 Nucl. Inst. Meth. Phys. Res. B 266 1173
[3] Kubankin A S, Nasonov N N 2008 J. Surf. Investig. X Ra. 2 317
[4] Tabrizi M, Korol A V, Solovyov A V 2007 Phys. Rev. Lett. 98 164801
[5] Korol A V, Solovyov A V, Greiner W 2007 Int. J. Mod. Phys. E 13 867
[6] Sushko G B, Korol A V, Greiner W, Solov’yov A V 2013 J. Phys.: Conf. Ser. 438 012018
[7] Korol A V, Solov’yov A V, Greiner W 2013 Channeling and Radiation in Periodically Bent Crystals, Springer Series on Atomic, Optical, and Plasma Physics (Berlin: Splinger) p195
[8] Gennady B S, Bezchastnov V G, Solovyov I A, Korol A V, Greiner W, Solovyov A V 2013 J. Comput. Phys. 252 404
[9] Luo S Y, Shao M Z, Luo X H 2010 Sci. China: Phys. Mech. Astron. 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学: 物理学, 力学和天文学 40 207]
[10] Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin. 59 2685 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 59 2685]
[11] Luo X H, Wu M Y, Li H T, Shao M Z, Xiong J Z, Luo S Y, He W 2011 Chin. J. Solid Mech. 32 440 (in Chinese) [罗晓华, 吴木营, 李洪涛, 邵明珠, 熊金志, 罗诗裕, 何为 2011 固体力学学报 32 440]
[12] Luo X H, He W, Shao M Z 2008 High Power Laser and Particle Beams 20 675 (in Chinese) [罗晓华, 何为, 邵明珠 2008 强激光与粒子束 20 675]
[13] Luo S Y, Shao M Z 2005 Chin. J. Seimcond. 26 294 (in Chinese) [罗诗裕, 邵明珠 2005 半导体学报 26 294]
[14] Li X P, Wang S J, Chen Q, Luo S Y 2013 Seim. Optoelectron. 34 441 (in Chinese) [李秀平, 王善进, 陈琼, 罗诗裕 2013 半导体光电 34 441]
[15] Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[16] Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[17] Nayfeh A H 1981 Introduction to Peturbation Techniques (London: John Wiley and Sons.) p226
[18] Grishchenko A D, Vavriv D M 1997 Zh. Tekh. Fiz. 67 1 (in Russia)
[19] Vavriv D M, Vavriv D D 2008 Proceedings of Ultrawideband and Ultrashort Impulse Signals Sevastopol, Ukraine, September 15–19, 2008 p16
[20] Wolf A, Swift J B, Vastano J A, Sminney H L 1985 Physica D 16 285
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