Angular homeostasis VII: non-monotonic correction systems.

E A Murphy; K R Berger

doi:10.1002/ajmg.1320390424

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Angular homeostasis VII: non-monotonic correction systems.

E A Murphy·K R Berger

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Abstract

We extend our model of angular homeostasis to correction functions that have a single maximum at a discrepant angle less than pi radians. We find that there are stable, and asymptotically stable, solutions that in general consist of self-intersecting curves. We investigate conditions for these curves to be periodic, and describe their symmetries. One typical pattern of such a closed curve involves a finite number of loops, each having a reflection axis of symmetry, with the complete curve having a cyclic rotation group. These bear a close resemblance to patterns found in lobulated biological structures (such as the petals of a flower or the primitive fetal hand). We further discuss implications for morphogenesis.

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Animals Homeostasis Mathematics Models, Biological Morphogenesis Journal Article Research Support, U.S. Gov't, P.H.S.

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E A Murphy, K R Berger. 1991-06-15. Angular homeostasis VII: non-monotonic correction systems.. https://doi.org/10.1002/ajmg.1320390424

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