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We have addressed numerically and analytically the diffusion mechanism of Turing pattern formation for the chlorine-iodine-malonic-acid system with a local concentration depended diffusivity (LCDD) in a two-dimensional space as well as its reciprocal counterpart. It is found that the Turing pattern develops in a normal way of Fickian diffusion when LCDD is not involved, namely with a zero LCDD adjusting parameter. The formation of a Turing pattern evolves in an abnormal way of either subdiffusion or superdiffusion when a non-zero LCDD adjusting parameter is taken into account, and a negative or a positive value of LCDD parameter corresponds to a subdiffusion or a superdiffusion. The sensitivity of the steady amplitude of the activator concentration of a Turing system to a random initial condition increases with increasing LCDD parameter.
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Keywords:
- reaction diffusion system /
- pattern /
- diffusion mechanism
[1] Lengyel I, Epstein I R 1991 Science 251 650
[2] Rudovics B, Barillot E, Davies P D, Dulos E, Boissonade J, Kepper D P 1999 J. Phys. Chem. A 103 1790
[3] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) pp1-4 (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1–4页]
[4] Ouyang Q, Swinney H L 1991 Nature 352 610
[5] Muñuzuri A P, Dolnik M, Zhabotinsky A M, Epstein I R 1999 J. Am. Chem. Soc. 121 8065
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[7] Chen J X, Zhang H, Li Y Q 2009 J. Chem. Phys. 130 124510
[8] Chen W Q, Zhang H, Ying H P, Li B W, Chen J X 2007 J. Chem. Phys. 127 154708
[9] Lesmes F, Hochberg D, Morán F, Pérez-Mercader J 2003 Phys. Rev. Lett. 91 238301
[10] Alonso S, Sagués F 2009 Phys. Rev. E 80 035203(R)
[11] Wang W M, Liu H Y, Cai Y L, Li Z Q 2011 Chin. Phys. B 20 074702
[12] He Y F, Liu F C, Fan W L, Dong L F 2012 Chin. Phys. B 21 034701
[13] Sun G Q, Jin Z, Liu Q X, Li L 2008 Chin. Phys. B 17 3936
[14] Yang L F, Epstein I R 2003 Phys. Rev. Lett. 90 178303
[15] Woolley T E, Baker R E, Gaffney E A, Maini P K 2011 Phys. Rev. E 84 041905
[16] Catllá A J, McNamara A, Topaz C M 2012 Phys. Rev. E 85 026215
[17] Shoji H, Iwasa Y, Mochizuki A, Kondo S 2002 J. Theor. Biol. 214 549
[18] Shoji H, Mochizuki A, Iwasa Y, Hirata M, Watanabe T, Hioki S, Kondo S 2003 Dev. Dyn. 226 627
[19] Shoji H, Iwasa Y, Kondo S 2003 J. Theor. Biol. 224 339
[20] Roussel M R, Wang J 2004 J. Chem. Phys. 120 8079
[21] Roussel M R, Wang J 2001 Phys. Rev. Lett. 87 188302
[22] Kuntz M, Lavallee P 2003 J. Phys. D: Appl. Phys. 36 1135
[23] Kuntz M, Lavallee P 2004 J. Phys. D: Appl. Phys. 37 L5
[24] Li W S, Hu W Y, Pang Y C, Liu T R, Zhong W R, Shao Y Z 2012 Phys. Rev. E 85 066132
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[1] Lengyel I, Epstein I R 1991 Science 251 650
[2] Rudovics B, Barillot E, Davies P D, Dulos E, Boissonade J, Kepper D P 1999 J. Phys. Chem. A 103 1790
[3] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) pp1-4 (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1–4页]
[4] Ouyang Q, Swinney H L 1991 Nature 352 610
[5] Muñuzuri A P, Dolnik M, Zhabotinsky A M, Epstein I R 1999 J. Am. Chem. Soc. 121 8065
[6] Horváth A K, Dolnik M, Muñuzuri A P, Zhabotinsky A M, Epstein I R 1999 Phys. Rev. Lett. 83 2950
[7] Chen J X, Zhang H, Li Y Q 2009 J. Chem. Phys. 130 124510
[8] Chen W Q, Zhang H, Ying H P, Li B W, Chen J X 2007 J. Chem. Phys. 127 154708
[9] Lesmes F, Hochberg D, Morán F, Pérez-Mercader J 2003 Phys. Rev. Lett. 91 238301
[10] Alonso S, Sagués F 2009 Phys. Rev. E 80 035203(R)
[11] Wang W M, Liu H Y, Cai Y L, Li Z Q 2011 Chin. Phys. B 20 074702
[12] He Y F, Liu F C, Fan W L, Dong L F 2012 Chin. Phys. B 21 034701
[13] Sun G Q, Jin Z, Liu Q X, Li L 2008 Chin. Phys. B 17 3936
[14] Yang L F, Epstein I R 2003 Phys. Rev. Lett. 90 178303
[15] Woolley T E, Baker R E, Gaffney E A, Maini P K 2011 Phys. Rev. E 84 041905
[16] Catllá A J, McNamara A, Topaz C M 2012 Phys. Rev. E 85 026215
[17] Shoji H, Iwasa Y, Mochizuki A, Kondo S 2002 J. Theor. Biol. 214 549
[18] Shoji H, Mochizuki A, Iwasa Y, Hirata M, Watanabe T, Hioki S, Kondo S 2003 Dev. Dyn. 226 627
[19] Shoji H, Iwasa Y, Kondo S 2003 J. Theor. Biol. 224 339
[20] Roussel M R, Wang J 2004 J. Chem. Phys. 120 8079
[21] Roussel M R, Wang J 2001 Phys. Rev. Lett. 87 188302
[22] Kuntz M, Lavallee P 2003 J. Phys. D: Appl. Phys. 36 1135
[23] Kuntz M, Lavallee P 2004 J. Phys. D: Appl. Phys. 37 L5
[24] Li W S, Hu W Y, Pang Y C, Liu T R, Zhong W R, Shao Y Z 2012 Phys. Rev. E 85 066132
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