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用双层耦合的Lengel-Epstein模型, 研究了两个子系统的图灵模对斑图的影响,发现其波数比在斑图的形成和选择过程中起着重要作用.当波数比为1时,双层系统未能发生耦合,只能出现条纹和六边形斑图;当波数比处于1-√17 的范围时,两子系统发生耦合,图灵模之间发生共振相互作用,得到种类丰富的超点阵斑图,包括暗点、点-棒和复杂超六边、Ⅰ-型和Ⅱ-型白眼、类蜂窝和环状超六边等斑图;当波数比大于√17 , 系统选择的斑图类型不再变化,均为环状超六边斑图.数值模拟得到的条纹、六边形、超六边点阵、Ⅱ-型白眼斑图和类蜂窝斑图均已在介质阻挡放电系统实验中观察到. 另外,还得到了超点阵斑图的波数随两个扩散系数乘积DuDv的变化曲线,发现其随的DuDv增大而减小.
[1] Barrio R A, Varea C, Aragon J L, Maini P K 1999 Math. Biol. 61 483
[2] Maini P K, Painter K J, Chau J 1999 Chem. Soc. Faraday Trans. 93 3601
[3] Epstein T, Fineberg J 2008 Phys. Rev. Lett. 100 134101
[4] Conway J M, Riecke H 2007 Phys. Rev. Lett. 99 218301
[5] Conway J M, Riecke H 2007 Phys. Rev. E 76 057202
[6] Hu H X, Li Q S, Ji L 2008 Phys. Chem. Chem. Phys. 10 438
[7] Dong L F, Xie W X, Zhao H T, Fan W L, He Y F, Xiao H 2009 Acta Phys. Sin. 58 4806 (in Chinese) [董丽芳、谢伟霞、赵海涛、范伟丽、贺亚峰、肖 红 2009 物理学报 58 4806]
[8] Dong L F, Zhao H T, Xie W X, Wang H F, Liu W L, Fan W L, Xiao H 2008 Acta Phys. Sin. 57 5768 (in Chinese) [董丽芳、赵海涛、谢伟霞、王红芳、刘微粒、范伟丽、肖 红 2008 物理学报 57 5768]
[9] Dong L F, Liu W L, Wang H F, He Y F, Fan W L, Gao R L 2007 Phys. Rev. E 76 046210
[10] He Y F, Dong L F, Liu W L, Wang H F, Zhao Z C, Fan W L 2007 Phys. Rev. E 76 017203
[11] Dong L F, Fan W L, He Y F,Liu F C, Li S F, Gao R L, Wang L 2006 Phys. Rev. E 73 066206
[12] Shao X J, Ma Y, Li Y X, Zhang G J 2010 Acta Phys. Sin. 59 8747 (in Chinese) [邵先军、马 跃、李娅西、张冠军 2010 物理学报 59 8747]
[13] Xia G Q, Xue W H, Chen M L,Zhu Y, Zhu G Q 2011 Acta Phys. Sin. 60 015201 (in Chinese) [夏广庆、薛伟华、陈茂林、朱 雨、朱国强 2011 物理学报 60 015201]
[14] Doelman A, Van Harten A 1995 Nonlinear Dynamics and Pattern Formation in the Natural Environment (Longman) p223
[15] Schenk C P, Schutz P, Bode M, Purwins H G 1998 Phys. Rev. E 57 6480
[16] Barrio R A, Varea C, Aragon J L, Maini P K 1999 Bull. Math. Biol. 61 483
[17] Yang L F, Dolnik M, Zhabotinsky A M, Epstein I R 2002 Phys. Rev. Lett. 88 208303
[18] Zhou C X, Guo H Y, Ouyang Q 2002 Phys. Rev. E 65 036118
[19] Berenstein I, Yang L F, Dolnik M, Zhabotinsky A M, Epstein I R 2005 J. Phys. Chem. A 109 5382
[20] Yang L F, Dolnik M, Zhabotinsky A M, Epstein I R 2006 Chaos 16 037114
[21] Bachir M, Metens S, Borckmans P, Dewel G 2001 Europhys. Lett. 54 612
[22] Page K M, Maini P K, Monk N A M 2005 Physica D 202 95
[23] Lengyel I, Epstein I R 1991 Science 251 650
[24] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific & Technological Education Publishing House) p12 (in Chinese) [欧阳颀 2000 反应扩散系统中的斑图动力学(上海:上海科技教育出版社)第12页]
[25] Dong L F, Xiao H, Fan W L Zhao H T, Yue H 2010 IEEE Trans. on Plas. Sci. 38 2486
[26] Dong L F, Qi Y Y, Zhao Z C, Li Y H 2008 Plas. Sourc. Sci. Technol. 17 015015
[27] Francis F C 1974 Introduction to Plasma Physics(California: Plenum Press)p90
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[1] Barrio R A, Varea C, Aragon J L, Maini P K 1999 Math. Biol. 61 483
[2] Maini P K, Painter K J, Chau J 1999 Chem. Soc. Faraday Trans. 93 3601
[3] Epstein T, Fineberg J 2008 Phys. Rev. Lett. 100 134101
[4] Conway J M, Riecke H 2007 Phys. Rev. Lett. 99 218301
[5] Conway J M, Riecke H 2007 Phys. Rev. E 76 057202
[6] Hu H X, Li Q S, Ji L 2008 Phys. Chem. Chem. Phys. 10 438
[7] Dong L F, Xie W X, Zhao H T, Fan W L, He Y F, Xiao H 2009 Acta Phys. Sin. 58 4806 (in Chinese) [董丽芳、谢伟霞、赵海涛、范伟丽、贺亚峰、肖 红 2009 物理学报 58 4806]
[8] Dong L F, Zhao H T, Xie W X, Wang H F, Liu W L, Fan W L, Xiao H 2008 Acta Phys. Sin. 57 5768 (in Chinese) [董丽芳、赵海涛、谢伟霞、王红芳、刘微粒、范伟丽、肖 红 2008 物理学报 57 5768]
[9] Dong L F, Liu W L, Wang H F, He Y F, Fan W L, Gao R L 2007 Phys. Rev. E 76 046210
[10] He Y F, Dong L F, Liu W L, Wang H F, Zhao Z C, Fan W L 2007 Phys. Rev. E 76 017203
[11] Dong L F, Fan W L, He Y F,Liu F C, Li S F, Gao R L, Wang L 2006 Phys. Rev. E 73 066206
[12] Shao X J, Ma Y, Li Y X, Zhang G J 2010 Acta Phys. Sin. 59 8747 (in Chinese) [邵先军、马 跃、李娅西、张冠军 2010 物理学报 59 8747]
[13] Xia G Q, Xue W H, Chen M L,Zhu Y, Zhu G Q 2011 Acta Phys. Sin. 60 015201 (in Chinese) [夏广庆、薛伟华、陈茂林、朱 雨、朱国强 2011 物理学报 60 015201]
[14] Doelman A, Van Harten A 1995 Nonlinear Dynamics and Pattern Formation in the Natural Environment (Longman) p223
[15] Schenk C P, Schutz P, Bode M, Purwins H G 1998 Phys. Rev. E 57 6480
[16] Barrio R A, Varea C, Aragon J L, Maini P K 1999 Bull. Math. Biol. 61 483
[17] Yang L F, Dolnik M, Zhabotinsky A M, Epstein I R 2002 Phys. Rev. Lett. 88 208303
[18] Zhou C X, Guo H Y, Ouyang Q 2002 Phys. Rev. E 65 036118
[19] Berenstein I, Yang L F, Dolnik M, Zhabotinsky A M, Epstein I R 2005 J. Phys. Chem. A 109 5382
[20] Yang L F, Dolnik M, Zhabotinsky A M, Epstein I R 2006 Chaos 16 037114
[21] Bachir M, Metens S, Borckmans P, Dewel G 2001 Europhys. Lett. 54 612
[22] Page K M, Maini P K, Monk N A M 2005 Physica D 202 95
[23] Lengyel I, Epstein I R 1991 Science 251 650
[24] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific & Technological Education Publishing House) p12 (in Chinese) [欧阳颀 2000 反应扩散系统中的斑图动力学(上海:上海科技教育出版社)第12页]
[25] Dong L F, Xiao H, Fan W L Zhao H T, Yue H 2010 IEEE Trans. on Plas. Sci. 38 2486
[26] Dong L F, Qi Y Y, Zhao Z C, Li Y H 2008 Plas. Sourc. Sci. Technol. 17 015015
[27] Francis F C 1974 Introduction to Plasma Physics(California: Plenum Press)p90
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