Heterogeneity-induced defect bifurcation and pulse dynamics for a three-component reaction-diffusion system.
Heterogeneity-induced defect bifurcation and pulse dynamics for a three-component reaction-diffusion system.
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DOI：
10.1103/physreve.75.036220
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
Xiaohui Yuan;T. Teramoto;Y. Nishiura
中科院分区：
文献类型：
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作者：
Xiaohui Yuan;T. Teramoto;Y. Nishiura
我们考虑的动力学时，旅行脉冲遇到一个激活剂-两个抑制剂类型的三组分反应扩散系统中的非均匀性，这通常是作为一个气体放电系统的定性模型。我们专注于的情况下，其中一个动力学系数的变化类似于一个平滑的阶梯函数，这是基本的更一般的异质性，在周期性或随机介质。由于非均匀性是以加性的方式引入动力学部分的，它导致系统产生各种类型的局部结构，平滑跳跃的非均匀性，称为跳跃点处的缺陷，这与Gray-Scott模型的乘法非均匀情况形成鲜明对比。主要研究行波脉冲与缺陷的碰撞动力学，并指出它们的全局分叉结构在阐明其内在机制中起着关键作用。碰撞后观察到五种输出，包括湮灭、反弹和钉扎。不稳定定态被认为是两个不同动力学区域之间的分离器：穿透和反弹，其作用非常接近于碰撞过程中产生的散射。提出了一个组织中心，通过对参数的展开产生行波脉冲、缺陷和标量。
We consider the dynamics when traveling pulses encounter heterogeneities in a three-component reaction diffusion system of one-activator-two-inhibitor type, which typically arises as a qualitative model of a gas-discharge system. We focused on the case where one of the kinetic coefficients changes similar to a smoothed step function, which is basic for more general heterogeneity as in periodic or random media. Since the heterogeneity is introduced to the kinetic part in an additive way, it causes the system to produce various types of localized structures smoothing the jump heterogeneity called the defects at the jump point, which makes a sharp contrast with the multiplicative heterogeneous case for the Gray-Scott model. The main issue is to study the collision dynamics between traveling pulses and defects, and show that their global bifurcation structure plays a key role in clarifying the underlying mechanism. Five outputs are observed after collisions including annihilation, rebound, and pinning. Unstable steady states are identified as separators between two different dynamic regimes: penetration and rebound, the role of which is very close to that of scattors arising in collision process. An organizing center producing the traveling pulses, defects, and scattors via unfolding with respect to the parameters is also presented.