Abstract
A model of seed population dynamics proposed by S. A. Levin, A. Hastings, and D. Cohen is presented and analyzed. With the environment considered as a mosaic of patches, patch age is used along with time as an independent variable. Local dynamics depend not only on the local state, but also on the global environment via dispersal modelled by an integral over all patch ages. Basic technical properties of the time varying solutions are examined; necessary and sufficient conditions for nontrivial steady states are given; and general sufficient conditions for global asymptotic stability of these steady states are established. Primary tools of analysis include a hybrid Picard iteration, fixed point methods, monotonicity of solution structure, and upper and lower solutions for differential equations.
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This work was supported in part by National Science Foundation Grants MCS-7903497 and MCS-790349701
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Elderkin, R.H. Seed dispersal in a patchy environment with global age dependence. J. Math. Biology 13, 283–303 (1982). https://doi.org/10.1007/BF00276065
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DOI: https://doi.org/10.1007/BF00276065