Spot bifurcations in three-component reaction-diffusion systems: The onset of propagation
Spot bifurcations in three-component reaction-diffusion systems: The onset of propagation
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三组分反应扩散系统中的点分叉：传播的开始
DOI：
10.1103/physreve.57.6432
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发表时间：
1998
影响因子：
2.4
通讯作者：
Hans
中科院分区：
文献类型：
--
作者：
M. Or;M. Bode;C. Schenk;Hans
研究了具有一个激活剂和两个抑制剂的任意维三组分反应扩散系统的定常局部解到行进局部解的分叉问题。我们发现，增加其中一个抑制剂的时间常数会导致这样的分叉。对于包含全部平稳两分量模式的极限情况，分叉是超临界的，并且没有其他分叉在它之前。根据定常解的形状，预测了分叉点和分叉点附近的速度。利用多尺度摄动理论验证了行波解的存在性和稳定性。数值模拟与分析结果吻合较好。
We present an analytical investigation of the bifurcation from stationary to traveling localized solutions in a three-component reaction-diffusion system of arbitrary dimension with one activator and two inhibitors. We show that increasing one of the inhibitors' time constants leads to such a bifurcation. For a limit case, which comprises the full range of stationary two-component patterns, the bifurcation is supercritical and no other bifurcation precedes it. Bifurcation points and velocities close to the branching point are predicted from the shape of the stationary solution. Existence and stability of the traveling solution are checked by means of multiple scales perturbation theory. Numerical simulations agree with the analytical results.