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Bounds on the populations in the Dreitlein-Smoes model of oscillatory kinetic systems

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Abstract

The model recently proposed by Dreitlein and Smoes for oscillatory kinetic systems is studied. Diffusion of the oscillating species is taken into account, and bounds on the total number of individuals of each species are determined for both two- and three-dimensional finite regions with various boundary conditons applied. It is found that in general the effect of diffusion on the system behavior is to reduce the maximum possible radius of limit cycles. In particular, in some cases global limit cycle behavior is precluded.

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Author notes

  1. Richard G. Fizell

    Present address: Systems Analysis and Engineering Department, Naval Air Development Center, 18974, Warminster, PA, U.S.A.

Authors and Affiliations

  1. Department of Physics, Drexel University, Philadelphia, PA, U.S.A.

    Richard G. Fizell

  2. Systems Analysis and Engineering Department, Naval Air Development Center, 18974, Warminster, PA, U.S.A.

    Paul E. Rubin

Authors
  1. Richard G. Fizell
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  2. Paul E. Rubin
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Fizell, R.G., Rubin, P.E. Bounds on the populations in the Dreitlein-Smoes model of oscillatory kinetic systems. Bltn Mathcal Biology 38, 623–631 (1976). https://doi.org/10.1007/BF02458637

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  • DOI: https://doi.org/10.1007/BF02458637

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