| TARGET PATTERNS AND SPIRAL WAVES IN REACTION-DIFFUSION SYSTEMS WITH LIMIT CYCLE KINETICSAND WEAK DIFFUSION |
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| 引用本文： | 赵晓强. TARGET PATTERNS AND SPIRAL WAVES IN REACTION-DIFFUSION SYSTEMS WITH LIMIT CYCLE KINETICSAND WEAK DIFFUSION[J]. 应用数学学报(英文版), 1998, 14(4): 347-357. DOI: 10.1007/BF02683817 |
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| 作者姓名： | 赵晓强 |
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| 作者单位： | ZHAO XIAOQIANG (Institute of Applied Mathematics，the Chinese Academy of Sciences，Beijing 100080，China)B.D. SLEEMAN(Department of Applied Mathematics，University of Leeds，Leeds LS2 9JT，United Kingdom) |
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| 摘 要： | 1.IntroductionTargetpatternsandspiralwavesarecommonlyobservedincertainmodelsofchemicalandbiologicalsystemssuchastheBelousov-ZhabotinskiireactionandthesocialamoebasDictyosteliumdiscoideium(of.11--4]andthereferencestherein).Thesesystemsaregovernedbyachemicalorbiologicalreactionandspatialdiffusion,i.e.reaction-diffusionequations.Generallyspeaking,atargetpatternisasetofconcentricringsofconstantconcentrationeachmovingoutward.Alonganyradialline,thepatternbehavesasymptoticallylikeaperiodictravellin…
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| 收稿时间： | 1995-07-21 |
Target patterns and spiral waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion |
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| Zhao Xiaoqiang,B. D. Sleeman. Target patterns and spiral waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion[J]. Acta Mathematicae Applicatae Sinica, 1998, 14(4): 347-357. DOI: 10.1007/BF02683817 |
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| Authors: | Zhao Xiaoqiang B. D. Sleeman |
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| Affiliation: | (1) Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080 Beijing, China;(2) Department of Applied Mathematics, University of Leeds, LS2 9JT Leeds, UK |
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| Abstract: | In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of nonlinear partial differential equation which is derived from singular perturbation techniques. We obtain the first order approximation expression of the dispersion curve for periodic wave trains and then show that in the generic case of limit cycle kinetics there is a one parameter family of target patterns and the rotating spiral waves of Archimedian type exist., Finally, we apply these results to the general λ−ω systems. |
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| Keywords: | Target patterns spiral waves reaction-diffusion systems and singular perturbation |
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