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Vegetative Flat Dryland Rhombic Pattern Formation Driven by Root Suction

In: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Author

Listed:
  • David J. Wollkind

    (Washington State University, Department of Mathematics)

  • Bonni J. Dichone

    (Gonzaga University, Department of Mathematics)

Abstract

A rhombic planform nonlinear cross-diffusive instability analysis is applied to an interaction-diffusion plant-ground water model system in an arid flat environment containing a root suction effect. A threshold-dependent paradigm is introduced to interpret stable rhombic patterns driven by this plant root suction effect in the ground water equation. The results of that analysis are represented by plots in a root suction coefficient versus rainfall rate dimensionless parameter space. From those plots regions corresponding to bare ground and vegetative patterns consisting of isolated patches, rhombic arrays of pseudo-spots or -gaps separated by an intermediate rectangular state, and homogeneous distributions from low to high density are identified in this parameter space. Then that morphological sequence, produced upon traversing an experimentally determined root suction characteristic curve, is compared with observational evidence relevant to the occurrence of leopard, pearled, or labyrinthine-type tiger bush, used to motivate an aridity classification scheme, and compared with some recent nonlinear vegetative pattern formation studies. There are four problems: The first two fill in some details of this analysis while the last two examine critical conditions for the onset of instability for a related vegetation model and rhombic pattern formation for an ion-sputtered solid surface erosion model.

Suggested Citation

  • David J. Wollkind & Bonni J. Dichone, 2017. "Vegetative Flat Dryland Rhombic Pattern Formation Driven by Root Suction," Springer Books, in: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, chapter 0, pages 457-487, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-73518-4_18
    DOI: 10.1007/978-3-319-73518-4_18
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