激励介质的非线性波型动力学(英文)  

Dynamics of Nonlinear Wave Pattern in Excitable Media

作　　者：周天寿[1] 张锁春[1] 

机构地区：[1]中国科学院数学与系统科学研究院,北京100080

出　　处：《中国科学院研究生院学报》2004年第2期276-281,共6页Journal of the Graduate School of the Chinese Academy of Sciences

摘　　要：以刻划著名的Belousov Zhabotinsky化学反应的俄勒冈振子为数学模型 ,研究解决了激励介质中一些悬而未决的理论问题 (如波的存在性和稳定性等 ) ,进一步完善了激励介质的非线性波型动力学的理论体系 .通过Painlev啨分析 ,B¨acklund变换和奇异摄动方法 ,分析地给出了一些常见的波型解 (如行波 ,螺旋波 ,靶型波 ,V 型波 ,涡卷波等 ) .在波前的邻域内 ,通过引进新的运动坐标系 ,获得了波在直角坐标下的运动方程 .特别是定量地给出了刻划小幅波的组织中心沿轴向和径向运动的规律 ,并由此可判定波的组织中心何时沿径向呈现膨胀或收缩 ,何时沿轴向有正向或反向漂移 .这一结果很好地与实验和数值模拟结果相吻合 .此外 ,研究了耦合的俄勒冈振子 ,解决了Tyson于 1 979年提出的一个猜想 (即对耦合的俄勒冈振子 ,稳定的回声波可以和稳定的正定态共存 ) ,提出了一套解决类似问题的一般方法 .Based on the Oregonator model portraying the famous Belousov-Zhabotinsky chemical reaction,the dynamics of nonlinear wave pattern in excitable media is further consummated.Some basic problems such as existence and stability of waves are studied.By Painlevé analysis,Bcklund transformation and pertubation method,some usual wave pattern solutions (for example, travelling wave,spiral wave,target wave,V-type wave,scroll wave,etc) are analytically presented.By establishing new moving coordinate systems in the neighborhood of the wave fornt,equations of motion of waves which describe the curvature effect of waves,are derived in the orthogonal coordinate system.In particular,law of motion of the organizing filament along the radial and axial directions,respectively,is quantitatively obtained.It demonstrates whether the filament expands or shrinks along the radial direction,and positively or inversely shifts along the axial direction.The result is in good accord with the existing experimental data.In addition,the coupled Oregonator is studied.Tyson's conjecture that the stable homogeneous positive steady state may coexist with the stable echo wave in the coupled model is basically solved.The corresponding proof procedure practically gives a general method in handling other similar problems.

关 键 词：激励介质 俄勒冈振子 BZ化学反应 波型解 组织中心 

分 类 号：O174[理学—数学] O175[理学—基础数学]