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In this paper, the antispiral and antitarget wave patterns in two-dimensional space are investigated numerically by Brusselator model with three components. The formation mechanism and spatiotemporal characteristics of these two waves are studied by analyzing dispersion relation and spatiotemporal variation of parameters of model equation. The influences of equation parameters on antispiral and antitarget wave are also analyzed. Various kinds of multi-armed antispiral are obtained, such as the two-armed, three-armed, four-armed, five-armed, and six-armed antispirals. The results show that antispirals may exist in a reaction-diffusion system, when the system is in the Hopf instability or the vicinity of wave instability. In addition to the above two types of instabilities, there is the Turing instability when the antitarget wave emerges. They have the periodicity in space and time, and their propagation directions are from outside to inward (the phase velocity vp 0), just as the incoming waves disappear in the center. The rotation directions of the various antispiral tips are the same as those of the waves, which can be rotated clockwise or anticlockwise, and the rotation period of wave-tip increases with the number of arms. Furthermore, it is found that the collision sequence of the multi-armed antispiral tip is related to the rotation direction of the wave-tip. With the increase of the number of anti-spiral arms, not only the dynamic behavior of the wave-tip turns more complex, but also the radius of the center region increases. Due to the influence of perturbation and boundary conditions, the multi-armed antispiral pattern can lose one arm and become a new antispiral pattern in the rotating process. Under certain conditions, it can be realized that the single-armed antispiral wave transforms into an antitarget wave. It is found that the change of control parameters of a and b can induce the regular changes of the space scale of antispiral waves, and antispiral waves gradually turn sparse with the increase of a, on the contrary, they gradually become dense with the increase of b. When the parameter of D_w exceeds a critical value, the propagation direction of wave is changed, and the system can produce the transformation from antispiral wave to spiral wave and from antitarget wave to target wave.
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Keywords:
- antispiral /
- antitarget /
- reaction-diffusion system /
- pattern
[1] Cysyk J, Tung L 2008 Biophys. J. 94 1533
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[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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[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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