Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources
Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources
复制标题
DOI：
10.1142/s0218127415501084
复制
发表时间：
2015-08
期刊：
影响因子：
--
通讯作者：
Jinliang Wang;Xiaojie Hou;Zhujun Jing
中科院分区：
文献类型：
--
作者：
Jinliang Wang;Xiaojie Hou;Zhujun Jing
本文研究了具有不同来源的活化剂-抑制剂型Gierer-Meinhardt模型的图灵模式。首先，我们研究了相应的动力学方程，推导了平衡稳定的条件，然后，我们将注意力转向系统的Hopf分岔。在一定参数范围内，均衡发生Hopf分岔；分岔是超临界的，分岔周期解是稳定的。当扩散系数足够大时，我们证明了平衡态和稳定态Hopf周期解都经历了图灵不稳定性。我们的数值模拟表明，图灵图案要么是斑点型，要么是条纹型。结果是新的。
In this paper, we study the Turing patterns in a Gierer–Meinhardt model of the activator–inhibitor type with different sources. First, we investigate the corresponding kinetic equations and derive the conditions for the stability of the equilibrium and then, we turn our attention to the Hopf bifurcation of the system. In certain parameter range, the equilibrium experiences a Hopf bifurcation; the bifurcation is supercritical and the bifurcated periodic solution is stable. With added diffusions, we show that both the equilibrium and the stable Hopf periodic solution experience Turing instability, if the diffusion coefficients of the two species are sufficiently different. Our numerical simulations show that the Turing patterns are either spot or stripe type. The results are new.