A hidden bifurcational structure for self-rlicating dynamics+

Yasumasa Nishiura, Daishin Ueyama

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1 Citation (Scopus)


Hidden bifurcational structure which drives the self-relicating tterns (SR) of reaction diffusion system is resented. Self-relicating dynamics on a finite interval can be regarded as a transient rocess from a localized trigger to a stable Turing attern or oscillatory Turing attern. SR looks like a cell division in two-dimensional sace. It is truly a transient henomenon in the sense that it only a ears temorarily on the way to the final attern. The resent aim is to give a new oint of view to describe such a transient dynamics of SREsecially we concentrate on the basic mechanism causing SR from a bifurcational view oint by emloying a new model system and its finite-dimensional comartment model which shares common features with the Gray-Scott model. The basic mechanism means how an oscillatory single ulse slits into two arts. It turns out that the essential dynamics of SR comes from the subcritical bifurcating loo of oscillatory branch of ulse tye. Any art of this loo does not aar in the hase sace; the aftereffect ot the limiting oint born from the subcriticality manifests the dynamics of SR.

Original languageEnglish
Pages (from-to)343-360
Number of pages18
JournalACH - Models in Chemistry
Issue number3
Publication statusPublished - 1998 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Chemistry(all)


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