Chaotic Pulses for Discrete Reaction Diffusion Systems
Chaotic Pulses for Discrete Reaction Diffusion Systems
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DOI：
10.1137/040608714
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Y. Nishiura;D. Ueyama;T. Yanagita
中科院分区：
文献类型：
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作者：
Y. Nishiura;D. Ueyama;T. Yanagita
讨论了一维晶格上混沌脉冲的存在性和动力学性质。行波脉冲通常出现在反应扩散系统中，如FitzHugh-Nagumo方程。这样的脉冲在相互碰撞时会湮灭。最近在许多系统中发现了一种新型的行波脉冲，脉冲像弹性球一样反弹。我们考虑一维晶格上的这种局域模式的行为，即，具有扩散型最近交互作用的常微分方程的无限系统。除了通常的驻波和行波脉冲，一种新的局域模式，它在晶格上混沌运动，数值发现。以扩散相互作用强度作为分岔参数，发现从驻波脉冲到混沌脉冲的路径是间歇型的。如果两个混沌脉冲在适当的时间发生碰撞，它们就会形成一个周期性的振荡脉冲，称为分子脉冲。数值研究了多个混沌脉冲之间的相互作用。
Existence and dynamics of chaotic pulses on a one-dimensional lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh-Nagumo equations. Such pulses annihilate when they collide with each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off like elastic balls. We consider the behavior of such a localized pattern on one-dimensional lattice, i.e., an infinite system of ODEs with nearest interaction of diffusive type. Besides the usual standing and traveling pulses, a new type of localized pattern, which moves chaotically on a lattice, is found numerically. Employing the strength of diffusive interaction as a bifurcation parameter, it is found that the route from standing pulse to chaotic pulse is of intermittent type. If two chaotic pulses collide with appropriate timing, they form a periodic oscillating pulse called a molecular pulse. Interaction among many chaotic pulses is also studied numerically.