关键词: 反螺旋波/
反靶波/
反应扩散系统/
斑图
English Abstract
Numerical investigation on antispiral and antitarget wave in reaction diffusion system
Ni Zhi-Wei,Li Xin-Zheng,
Bai Zhan-Guo,
Li Yan
1.School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China
Fund Project:Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. A2017208081) and the Major Project of Educational Commission of Hebei Province, China (Grant No. ZD2016025).Received Date:02 May 2018
Accepted Date:29 June 2018
Published Online:20 September 2019
Abstract: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.
Keywords: antispiral/
antitarget/
reaction-diffusion system/
pattern
