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采用三变量Brusselator扩展模型在二维空间对反应扩散系统中反螺旋波和反靶波进行了数值模拟,利用色散关系和参量的时空变化研究了反螺旋波与反靶波的形成机制和时空特性,分析了方程参数对反螺旋波与反靶波的影响,获得了多种不同臂数的反螺旋波.模拟结果表明:反螺旋波源于波失稳、霍普失稳,或两种失稳的共同作用,而在反靶波中除上述两种失稳外还同时存在图灵失稳,波的传播方向均由外向内;反螺旋波波头的相位运动方向与波的走向相同,且旋转周期随臂数的增加逐渐增大;多臂数的反螺旋波由于受微扰及边界条件的影响,在波头的持续旋转运动中可以向臂数少的反螺旋波发生转变,并且在一定条件下单臂反螺旋波可实现到反靶波的转变;当不活跃中间物质的浓度的扩散系数超过临界值时,波的传播方向发生改变,系统可以实现反螺旋波到螺旋波以及反靶波到靶波的转变.
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[1] Cysyk J, Tung L 2008 Biophys. J. 94 1533
[2] Frisch T, Rica S, Coullet P, Gilli J M 1994 Phys. Rev. Lett. 72 1471
[3] Lodahl P, Bache M, Saffman M 2000 Phys. Rev. Lett. 85 4506
[4] Sawai S, Thomason P A, Cox E C 2005 Nature 433 323
[5] Zaritski R M, Pertsov A M 2002 Phys. Rev. E 66 066120
[6] Guo H Y, Li L, Ouyang Q 2003 J. Chem. Phys. 118 5038
[7] Cai M C, Pan J T, Zhang H 2014 Phys. Rev. E 89 022920
[8] Hendrey M, Ott E, Antonsen T M 2000 Phys. Rev. E 61 4943
[9] Vaidelys M, Lu C, Cheng Y J, Ragulskis M 2017 Physica A 467 1
[10] Wang P, Li Q Y, Tang G N 2018 Acta Phys. Sin. 67 030502 (in Chinese) [汪芃, 李倩昀, 唐国宁 2018 物理学报 67 030502]
[11] Ma J, Xu Y, Wang C N, Jin W Y 2016 Physica A 461 586
[12] Li T C, Gao X, Zheng F F, Pan D B, Zheng B, Zhang H 2017 Sci. Rep. 7 8657
[13] Yuan G Y, Zhang H, Wang G R 2013 Acta Phys. Sin. 62 160502 (in Chinese) [袁国勇, 张焕, 王光瑞 2013 物理学报 62 160502]
[14] Liu W B, Dong L F 2015 Acta Phys. Sin. 64 245202 (in Chinese) [刘伟波, 董丽芳 2015 物理学报 64 245202]
[15] Vasiev B, Siegert F, Weijer C 1997 Phys. Rev. Lett. 78 2489
[16] Bursac N, Aguel F, Tung L 2004 Proc. Natl. Acad. Sci. 101 15530
[17] Deng L Y, Zhang H, Li Y Q 2009 Phys. Rev. E 79 036107
[18] Hagan P S 1982 Siam. J. Appl. Math. 42 762
[19] Gao J, Wang Q, L H P 2017 Chem. Phys. Lett. 685 205
[20] Vanag V K, Epstein I R 2001 Science 294 835
[21] Gong Y F, Christini D J 2003 Phys. Rev. Lett. 90 088302
[22] Wang C, Zhang C X, Ouyang Q 2006 Phys. Rev. E 74 036208
[23] Nicola E M, Brusch L, Br M 2004 J. Phys. Chem. B 108 14733
[24] Qian Y, Huang X D, Liao X H, Hu G 2010 Chin. Phys. B 19 050513
[25] Yang L F, Epstein I R 2002 J. Phys. Chem. A 106 11676
[26] Vanag V K, Epstein I R 2002 Phys. Rev. Lett. 88 088303
[27] Plapp B B, Bodenschatz E 1996 Phys. Scr. 1996 111
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