-
The influence of Turing modes in two subsystems on pattern formation is investigated by using the two-layer coupled Lengel-Epstein model. It is found that the wave number ratio between two Turing modes play an important role in the pattern formation and pattern selection. When the wave number ratio is 1, no coupling behavior occurs between two subsystems and only stripe and hexagon patterns arise in system. If the wave number ratio lies in a range of 1-√17, a variety of superlattice patterns, such as dark-dot, bar-dot and complex super hexagons, I-type or II-type white-eye, honeycomb-like, and superhexagon of circle, are obtained due to the resonance interaction between the two Turing modes in the coupled systems. When the wave number ratio is greater than √17, the superhexagon of circle is always selected and unchanged. Some superlattice patterns above, including stripes, hexagons, super hexagon, Ⅱ-type white-eye, and honeycomb-like patterns, are observed experimentally in a dielectric barrier discharge (DBD) system. In addition, the curves for variation of hexagon pattern wave number with the increase of the product of two diffusion coefficients are obtained and it is found that the wave number becomes smaller with DuDv increasing.
[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 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 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 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 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
-
[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 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 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 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 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
Catalog
Metrics
- Abstract views: 8571
- PDF Downloads: 638
- Cited By: 0
下载:
