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Understanding the patterns in the BZ reagent

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Conclusion

It has been pretty well established that the PC system examined in this talk is a realistic model for the spatially distributed BZ reagent under commonly occurring parameter conditions. The analysis of the system is straightforward and provides a clear picture of the mechanism behind the appearance of fronts, trains, solitary pulses, and target patterns, and behind the generation of spirals, under those conditions. In fact, the PC model has been remarkable successful in reflecting observed phenomena (see a discussion of this point in Ref. 34). Spiral-like structures in 3-space have been called scrolls by A. Winfree; their generation can also be easily understood along these same lines, as resulting from local disturbances of plane solitary waves propagating through 3-space. Fully developed spirals can likely be understood in this same PC context as solutions of the free boundary problem presented in Section 7; more mathematical and numerical work should be done on that problem.

Very possibly other parameter conditions exist for which similar spatial patterns can be seen in the BZ reagent, but for which the PC framework is not appropriate; and very likely other excitable biological or chemical media, supporting such patterns, may require other models for their understanding. Nevertheless, it appears likely that models having many of the properties of the one studied here will play a significant role in the unraveling of these more complex systems.

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  1. Mathematics Department, University of Arizona, 85721, Tucson, Arizona

    Paul C. Fife

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Fife, P.C. Understanding the patterns in the BZ reagent. J Stat Phys 39, 687–703 (1985). https://doi.org/10.1007/BF01008360

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